The Geometry of Walker Manifolds

* Basic Algebraic Notions* Basic Geometrical Notions* Walker Structures* Three-Dimensional Lorentzian Walker Manifolds* Four-Dimensional Walker Manifolds* The Spectral Geometry of the Curvature Tensor* Hermitian Geometry* Special Walker Manifolds

[1]  Henrik Pedersen,et al.  The Ledger curvature conditions and D'Atri geometry , 1999 .

[2]  Oldřich Kowalski,et al.  Riemannian Metrics with the Prescribed Curvature Tensor and all Its Covariant Derivatives at One Point , 2006 .

[3]  Peter B. Gilkey,et al.  The Jordan normal form of Osserman algebraic curvature tensors , 2001 .

[4]  M Brozos-V Pseudo-riemannian Manifolds with Commuting Jacobi Operators , .

[5]  M Brozos-V Manifolds with Commuting Jacobi Operators , .

[6]  Lieven Vanhecke,et al.  Riemannian Manifolds of Conullity Two , 1996 .

[7]  Oldřich Kowalski,et al.  A Classification of Locally Homogeneous Affine Connections with Skew-Symmetric Ricci Tensor on 2-Dimensional Manifolds , 2000 .

[8]  Yung-Chow Wong Two dimensional linear connexions with zero torsion and recurrent curvature , 1964 .

[9]  Franki Dillen,et al.  A Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric , 2001 .

[10]  Yasuo Matsushita Walker 4-manifolds with proper almost complex structures , 2005 .

[11]  C. W. Mitchell Ads Pp-waves , 2005 .

[12]  小平 邦彦,et al.  Global analysis : papers in honor of K. Kodaira , 2015 .

[13]  Peter B. Gilkey,et al.  Riemannian manifolds whose skewd-symmetric curvature operator has constant eigenvalues , 1999 .

[14]  Ramón Vázquez-Lorenzo,et al.  Almost Kähler Walker 4-manifolds , 2007 .

[15]  Giovanni Calvaruso Addendum to “Homogeneous structures on three-dimensional Lorentzian manifolds” [J. Geom. Phys. 57 (2007) 1279–1291] , 2008 .

[16]  E. García‐Río,et al.  Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[17]  H. Wu,et al.  On the de Rham decomposition theorem , 1964 .

[18]  Andrzej Derdzinski,et al.  Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case , 2002, math/0211248.

[19]  Hirosi Ooguri,et al.  Geometry of N=2 strings , 1991 .

[20]  Luis Hernández-lamoneda,et al.  Curvature vs. Almost Hermitian Structures , 2000 .

[21]  Stefan Ivanov,et al.  Riemannian Manifolds in Which Certain Curvature Operator Has Constant Eigenvalues along Each Circle , 1997 .

[22]  Yasuo Matsushita,et al.  Hitchin–Thorpe-Type Inequalities for Pseudo-Riemannian 4-Manifolds of Metric Signature (++−−) , 2001 .

[23]  P. Gilkey,et al.  GEOMETRIC REALIZATIONS OF CURVATURE MODELS BY MANIFOLDS WITH CONSTANT SCALAR CURVATURE , 2008, 0811.1651.

[24]  J. Shah,et al.  VECTOR FIELDS ON SPHERES , 2007 .

[25]  Charles P. Boyer,et al.  A note on hyperhermitian four-manifolds , 1988 .

[26]  Neda Bokan,et al.  A Note on Osserman Lorentzian Manifolds , 1997 .

[27]  Kazumi Tsukada,et al.  Three-dimensional conformally flat homogeneous Lorentzian manifolds , 2007 .

[28]  I. Holopainen Riemannian Geometry , 1927, Nature.

[29]  Quo-Shin Chi Curvature characterization and classification of rank-one symmetric spaces. , 1991 .

[30]  Giovanni Calvaruso,et al.  Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues , 2008 .

[31]  Eduardo García-Río,et al.  Four-dimensional indefinite Kähler Osserman manifolds , 2005 .

[32]  Ramón Vázquez-Lorenzo,et al.  Osserman Manifolds in Semi-Riemannian Geometry , 2002 .

[33]  John Armstrong,et al.  An ansatz for almost-Kähler, Einstein 4-manifolds , 2002 .

[34]  Hitoshi Takagi,et al.  On conformally flat spaces satisfying a certain condition on the Ricci tensor , 1971 .

[35]  T. Y. Thomas The decomposition of Riemann spaces in the large , 1939 .

[36]  Z. Szabó,et al.  A short topological proof for the symmetry of 2 point homogeneous spaces , 1991 .

[37]  P. Gilkey,et al.  Geometric realizations of Hermitian curvature models , 2008, 0812.2743.

[38]  Bernd Fiedler Determination of the structure of algebraic curvature tensors by means of Young symmetrizers , 2002, ArXiv.

[39]  Lieven Vanhecke,et al.  Curvature homogeneity for four-dimensional manifolds , 1995 .

[40]  P. Gilkey,et al.  The classification of simple Jacobi--Ricci commuting algebraic curvature tensors , 2007 .

[41]  J. Milnor Curvatures of left invariant metrics on lie groups , 1976 .

[42]  Peter B. Gilkey,et al.  The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds , 2007 .

[43]  Ramón Vázquez-Lorenzo,et al.  New examples of Osserman metrics with nondiagonalizable Jacobi operators , 2006 .

[44]  Boris Khesin,et al.  Symplectic and Contact Topology: Interactions and Perspectives , 2003 .

[45]  Corey Dunn,et al.  Curvature Homogeneous Pseudo-Riemannian Manifolds which are not Locally Homogeneous , 2005 .

[46]  Jimmy Petean Indefinite Kähler-Einstein Metrics on Compact Complex Surfaces , 1997 .

[47]  Giovanni Calvaruso,et al.  Homogeneous structures on three-dimensional Lorentzian manifolds , 2007 .

[48]  Eduardo García-Río,et al.  Four-dimensional manifolds with degenerate self-dual Weyl curvature operator , 2008 .

[49]  Jurgen Berndt Three-dimensional Einstein-like manifolds , 1992 .

[50]  Mohammad Reza Chaichi,et al.  Three-dimensional Lorentz manifolds admitting a parallel null vector field , 2005 .

[51]  Stefan Ivanov,et al.  ParaHermitian and paraquaternionic manifolds , 2005 .

[52]  Adam Chudecki,et al.  From hyperheavenly spaces to Walker and Osserman spaces: I , 2008 .

[53]  Stana Nikcevic,et al.  Generalized plane wave manifolds , 2005 .

[54]  Alfred Gray,et al.  Einstein-like manifolds which are not Einstein , 1978 .

[55]  Ramón Vázquez-Lorenzo,et al.  Affine Osserman connections and their Riemann extensions , 1999 .

[56]  Jacques Lafontaine Conformal Geometry from the Riemannian Viewpoint , 1988 .

[57]  A. G. Walker CONNEXIONS FOR PARALLEL DISTRIBUTIONS IN THE LARGE , 1955 .

[58]  Quo-Shin Chi,et al.  A curvature characterization of certain locally rank-one symmetric spaces , 1988 .

[59]  Ramón Vázquez-Lorenzo,et al.  Lorentzian three-manifolds with special curvature operators , 2008 .

[60]  S. Rahmani,et al.  Métriques de lorentz sur les groupes de lie unimodulaires, de dimension trois , 1992 .

[61]  P. Gilkey,et al.  Geometric realizations of generalized algebraic curvature operators , 2008, 0811.3180.

[62]  M. Gromov,et al.  Partial Differential Relations , 1986 .

[63]  Xinkai Wu,et al.  Dynamics of antimembranes in the maximally supersymmetric eleven-dimensional pp wave , 2006 .

[64]  Louis Nirenberg,et al.  Complex Analytic Coordinates in Almost Complex Manifolds , 1957 .

[65]  Grozio Stanilov Higher order Skew-symmetric and symmetric curvature operators , 2004 .

[66]  H. K. Nickerson On conformally symmetric spaces , 1985 .

[67]  Guosong Zhao,et al.  Global Affine Differential Geometry of Hypersurfaces , 1993 .

[68]  Peter B. Gilkey,et al.  Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor , 2001 .

[69]  Neil Marcus The N=2 open string , 1992 .

[70]  Graham Hall,et al.  Affine collineations in space‐time , 1988 .

[71]  L.Bérard Bergery,et al.  Sur l'holonomie des variétés pseudo-riemanniennes de signature (n, n) , 1997 .

[72]  Charles P. Boyer A note on hyper-Hermitian four-manifolds , 1988 .

[73]  Adil Belhaj,et al.  Superstring theory on pp waves with ADE geometries , 2005 .

[74]  Giovanni Calvaruso,et al.  Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds , 2007 .

[75]  Maciej Dunajski Anti-self-dual four–manifolds with a parallel real spinor , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[76]  Eduardo García-Río,et al.  On a problem of Osserman in Lorentzian geometry , 1997 .

[77]  D. Alekseevsky,et al.  Cones over pseudo-Riemannian manifolds and their holonomy , 2007, 0707.3063.

[78]  Ramón Vázquez-Lorenzo,et al.  OSSERMAN METRICS ON WALKER 4-MANIFOLDS EQUIPPED WITH A PARA-HERMITIAN STRUCTURE , 2007 .

[79]  Oldřich Kowalski,et al.  Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds , 2008 .

[80]  Maciej Dunajski,et al.  Anti-Self-Dual Conformal Structures in Neutral Signature , 2006, math/0610280.

[81]  Ramón Vázquez-Lorenzo,et al.  Four-Dimensional Osserman Symmetric Spaces , 2001 .

[82]  Yu. G. Nikonorov,et al.  On δ-homogeneous Riemannian manifolds , 2007, Springer Monographs in Mathematics.

[83]  P. Gilkey,et al.  Algebraic theory of affine curvature tensors , 2006 .

[84]  Santiago de Compostela,et al.  LEFT-INVARIANT LORENTZIAN METRICS ON 3-DIMENSIONAL LIE GROUPS , 1996 .

[85]  Lieven Vanhecke,et al.  Lorentz manifolds modelled on a Lorentz symmetric space , 1990 .

[86]  P. Gilkey,et al.  Pseudo-Riemannian Jacobi-Videv Manifolds , 2007, 0708.1096.

[87]  S. I. Goldberg,et al.  On conformally flat spaces with commuting curvature and Ricci transformations , 1972 .

[88]  Giovanni Calvaruso,et al.  Semi-symmetric Lorentzian metrics and three-dimensional curvature homogeneity of order one , 2009 .

[89]  L. A. Cordero,et al.  LATTICES AND PERIODIC GEODESICS IN PSEUDORIEMANNIAN 2-STEP NILPOTENT LIE GROUPS , 2008, 0802.3771.

[90]  Marek A. Abramowicz,et al.  Epicyclic Orbital Oscillations in Newton's and Einstein's Dynamics , 2002, gr-qc/0206063.

[91]  Robert S. Strichartz,et al.  Linear Algebra of Curvature Tensors and Their Covariant Derivatives , 1988, Canadian Journal of Mathematics.

[92]  Andrzej Derdzinski,et al.  Self-dual Kähler manifolds and Einstein manifolds of dimension four , 1983 .

[93]  Takashi Oguro,et al.  Four-Dimensional Almost Kähler Einstein and *-Einstein Manifolds , 1998 .

[94]  Lieven Vanhecke,et al.  Curvature invariants, differential operators and local homogeneity , 1996 .

[95]  R. Castro,et al.  Pseudo-Chern Classes and Opposite Chern Classes of Indefinite Almost Hermitian Manifolds , 1997 .

[96]  Andreas Koutras,et al.  A metric with no symmetries or invariants , 1996 .

[97]  J. Kluson,et al.  D-brane dynamics in a plane wave background , 2006 .

[98]  Peter B. Gilkey,et al.  Jacobi–Jacobi Commuting Models and Manifolds , 2009 .

[99]  Sorin Dragomir,et al.  Indefinite locally conformal Kähler manifolds , 2006 .

[100]  A. Montesinos Amilibia Degenerate Homogeneous Structures of Type $\S_1$ on Pseudo-Riemannian Manifolds , 2001 .

[101]  R. Castro,et al.  Pseudo-Riemannian manifolds with simple Jacobi operators , 2002 .

[102]  P. Gilkey,et al.  Projectively Osserman manifolds , 2007 .

[103]  Neda Bokan,et al.  Osserman pseudo-Riemannian manifolds of signature (2,2) , 2001, Journal of the Australian Mathematical Society.

[104]  Yaron Oz,et al.  Families of N = 2 strings , 2002 .

[105]  A. Jevicki,et al.  Large N field theory of N=2 strings and self-dual gravity , 1999 .

[106]  P. Gilkey,et al.  CONFORMALLY OSSERMAN MANIFOLDS AND CONFORMALLY COMPLEX SPACE FORMS , 2004 .

[107]  Robert L. Bryant,et al.  Bochner-Kahler metrics , 2000, math/0003099.

[108]  Graham Hall,et al.  Covariantly constant tensors and holonomy structure in general relativity , 1991 .

[109]  Tan Zhang,et al.  Manifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvalues , 2000 .

[110]  A. G. Walker Canonical form for a Riemannian space with a parallel field of null planes , 1950 .

[111]  Lieven Vanhecke,et al.  Examples of curvature homogeneous Lorentz metrics , 1997 .

[112]  Aaron Fialkow,et al.  Hypersurfaces of A Space of Constant Curvature , 1938 .

[113]  Bruce L. Reinhart,et al.  The second fundamental form of a plane field , 1977 .

[114]  Yuri Nikolayevsky,et al.  Osserman manifolds of dimension 8 , 2003 .

[115]  M. Brozos-Vazquez,et al.  Stanilov-Tsankov-Videv Theory ? , 2007 .

[116]  Udo Simon,et al.  Introduction to the affine differential geometry of hypersurfaces , 1991 .

[117]  Ramón Vázquez-Lorenzo,et al.  Hermitian–Walker 4-manifolds , 2008 .

[118]  Ramón Vázquez-Lorenzo,et al.  Four-dimensional Osserman–Ivanov–Petrova metrics of neutral signature , 2007 .

[119]  M Brozos-V The Global Geometry of Riemannian Manifolds with Commuting Curvature Operators , 2006 .

[120]  Tan Zhang,et al.  ALGEBRAIC CURVATURE TENSORS FOR INDEFINITE METRICS WHOSE SKEW-SYMMETRIC CURVATURE OPERATOR HAS CONSTANT JORDAN NORMAL FORM , 2002 .

[121]  Thomas Leistner Screen bundles of Lorentzian manifolds and some generalisations of pp-waves , 2006 .

[122]  Z. Afifi Riemann extensions of affine connected spaces , 1954 .

[123]  Pedro M. Gadea,et al.  Reductive homogeneous pseudo-Riemannian manifolds , 1997 .

[124]  Stefan Ivanov,et al.  Riemannian Manifold in Which the Skew-Symmetric Curvature Operator has Pointwise Constant Eigenvalues , 1998 .

[125]  Neda Bokan,et al.  A note on the Osserman conjecture and isotropic covariant derivative of curvature , 1999 .

[126]  S. I. Goldberg,et al.  Integrability of almost Kaehler manifolds , 1969 .

[127]  P. Gilkey,et al.  Complete curvature homogeneous pseudo-Riemannian manifolds , 2004 .

[128]  P. Gilkey,et al.  The spectral geometry of the Weyl conformal tensor , 2003 .

[129]  Peter Bueken,et al.  Three‐dimensional Riemannian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3 , 1996 .

[130]  Yasuo Matsushita,et al.  A Spinor Approach to Walker Geometry , 2008 .

[131]  Vivian De Smedt Decomposition of the curvature tensor of hyper-Kähler manifolds , 1994 .

[132]  Marek A. Abramowicz,et al.  Epicyclic oscillations of fluid bodies - II. Strong gravity , 2005 .

[133]  Edward J. Flaherty,et al.  Hermitian and Kahlerian geometry in relativity , 1975 .

[134]  Neda Bokan,et al.  Geometric Structures as Determined by the Volume of Generalized Geodesic Balls , 2003 .

[135]  V. Pravda,et al.  All spacetimes with vanishing curvature invariants , 2002 .

[136]  D. E. Blair,et al.  Isotropic Kähler hyperbolic twistor spaces , 2004 .

[137]  Charles P. Boyer,et al.  COMPLEX GENERAL RELATIVITY, H AND HH SPACES: A SURVEY OF ONE APPROACH , 1979 .

[138]  A. G. Walker ON PARALLEL FIELDS OF PARTIALLY NULL VECTOR SPACES , 1949 .

[139]  Andrzej Derdzinski,et al.  The local structure of conformally symmetric manifolds , 2007, 0704.0596.

[140]  E. Latini,et al.  Making the hyper-Kähler structure of N=2 quantum string manifest , 2004 .

[141]  Johann Davidov,et al.  Self-dual Walker metrics with a two-step nilpotent Ricci operator , 2006 .

[142]  Hiroyuki Kamada,et al.  Neutral hyperkahler structures on primary Kodaira surfaces , 1999 .

[143]  Peter Gilkey,et al.  Curvature Tensors Whose Jacobi or Szabó Operator is Nilpotent on Null Vectors , 2002 .

[144]  Peter B. Gilkey,et al.  Jordan Szabo algebraic covariant derivative curvature tensors , 2002 .

[145]  Peter B. Gilkey,et al.  Pseudo Riemannian manifolds whose generalized Jacobi operator has constant characteristic polynomial , 1998 .

[146]  P. Gilkey,et al.  Manifolds which are Ivanov-Petrova or k -Stanilov , 2003 .

[147]  Y. Nikolayevsky Riemannian manifolds whose curvature operator R(X, Y) has constant eigenvalues , 2004, Bulletin of the Australian Mathematical Society.

[148]  Alfonso Romero,et al.  Complex Einstein hypersurfaces of indefinite complex space forms , 1983, Mathematical Proceedings of the Cambridge Philosophical Society.

[149]  P. Gilkey,et al.  Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds , 2004 .

[150]  Hitoshi Takagi,et al.  ON CURVATURE HOMOGENEITY OF RIEMANNIAN MANIFOLDS , 1974 .

[151]  Oldřich Kowalski,et al.  A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach , 2004 .

[152]  Albert Marden,et al.  Outer Circles: An Introduction to Hyperbolic 3-Manifolds , 2007 .

[153]  Kyoko Honda,et al.  Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators , 2003 .

[154]  Mirjana Djorić,et al.  Three-Dimensional Lorentz Metrics and Curvature Homogeneity of Order One , 2000 .

[155]  Kazuo Yamato,et al.  Algebraic Riemann manifolds , 1989, Nagoya Mathematical Journal.

[156]  P. Gilkey,et al.  Jacobi--Tsankov manifolds which are not 2-step nilpotent , 2006 .

[157]  Alfred Gray,et al.  Curvature identities for Hermitian and almost Hermitian manifolds , 1976 .

[158]  Eric Bergshoeff,et al.  Self-dual supergravity theories in 2 + 2 dimensions , 1992, hep-th/9206101.

[159]  Andrzej Derdzinski,et al.  Non-Walker Self-Dual Neutral Einstein Four-Manifolds of Petrov Type III , 2008, 0809.0855.

[160]  Novica Blažić,et al.  Natural curvature operators of bounded spectrum , 2006 .

[161]  Peter Bueken,et al.  On curvature homogeneous three-dimensional Lorentzian manifolds , 1997 .

[162]  Yasuo Matsushita,et al.  Almost Kähler-Einstein Structures on 8-Dimensional Walker Manifolds , 2006 .

[163]  P. Gilkey,et al.  Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds. , 2006 .

[164]  Vestislav Apostolov,et al.  Generalized Goldberg-Sachs theorems for pseudo-Riemannian four-manifolds , 1998 .

[165]  Alfonso Romero,et al.  The Gauss-Landau-Hall problem on Riemannian surfaces , 2004 .

[166]  Peter B. Gilkey,et al.  Geometrical Representations of Equiaffine Curvature Operators , 2008 .

[167]  Igor Volovich,et al.  Anti-Kählerian manifolds , 2000 .

[168]  Gabriela P. Ovando,et al.  Invariant pseudo Kaehler metrics in dimension four , 2004, math/0410232.

[169]  Yuri Nikolayevsky,et al.  Osserman Conjecture in dimension n ≠ 8, 16 , 2005 .

[170]  Peter Giblin Arthur Geoffrey Walker 1909–2001 , 2004 .

[171]  Hans-Friedrich Münzner,et al.  Cliffordalgebren und neue isoparametrische Hyperflächen , 1981 .

[172]  Peter B. Gilkey Bundles over projective spaces and algebraic curvature tensors , 2001 .

[173]  Ramón Vázquez-Lorenzo,et al.  NONSYMMETRIC OSSERMAN PSEUDO-RIEMANNIAN MANIFOLDS , 1998 .

[174]  Alfred Gray,et al.  The sixteen classes of almost Hermitian manifolds and their linear invariants , 1980 .

[175]  Robert Osserman,et al.  Curvature in the eighties , 1990 .

[176]  Andrzej Derdzinski Chapter 4 – Einstein Metrics in Dimension Four , 2000 .

[177]  R. Castro,et al.  Nonsymmetric Osserman indefinite Kähler manifolds , 1998 .

[178]  P. Gilkey,et al.  Curvature homogeneous signature (2,2) manifolds , 2004 .

[179]  P. Gilkey,et al.  Examples of signature (2, 2) manifolds with commuting curvature operators , 2007, 0708.2770.

[180]  A. Martin,et al.  Indefinite Einstein hypersurfaces with nilpotent shape operators , 1984 .

[181]  Peter B. Gilkey,et al.  Manifolds whose curvature operator has constant eigenvalues at the basepoint , 1994 .

[182]  Akira Yamada,et al.  Compact indefinite almost Kähler Einstein manifolds , 2008 .

[183]  Vestislav Apostolov,et al.  The Riemannian Goldberg–Sachs Theorem , 1997 .

[184]  Giovanni Calvaruso Three-dimensional homogeneous Lorentzian metrics with prescribed Ricci tensor , 2007 .

[185]  Eduardo García-Río,et al.  A note on the structure of algebraic curvature tensors , 2004 .

[186]  Georges de Rham,et al.  Sur la réductibilité d'un espace de Riemann , 1952 .

[187]  P. Gilkey,et al.  Complete k-Curvature Homogeneous Pseudo-Riemannian Manifolds , 2005 .

[188]  Andrzej Derdzinski,et al.  Connections with Skew-Symmetric Ricci Tensor on Surfaces , 2008, 0802.0163.

[189]  Ramón Vázquez-Lorenzo,et al.  Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor , 2010, Canadian Journal of Mathematics.

[190]  Maria Ivanova,et al.  FOUR-DIMENSIONAL RIEMANNIAN MANIFOLDS WITH COMMUTING HIGHER ORDER JACOBI OPERATORS , 2007 .

[191]  Lieven Vanhecke,et al.  ISOPARAMETRIC GEODESIC SPHERES AND A CONJECTURE OF OSSERMAN CONCERNING THE JACOBI OPERATOR , 1995 .

[192]  Kouei Sekigawa,et al.  On some compact Einstein almost Kähler manifolds , 1987 .

[193]  Lieven Vanhecke,et al.  Four-dimensional curvature homogeneous spaces , 1992 .

[194]  Giovanni Calvaruso,et al.  Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One , 2010, Canadian Mathematical Bulletin.

[195]  Yury. Nikolayevsky Osserman manifolds and Clifford structures , 2003 .

[196]  Eduardo García-Río,et al.  Isotropic Kähler structures on Engel 4-manifolds , 2000 .

[197]  Vicente Cortés,et al.  A class of Osserman spaces , 2005 .

[198]  Ramón Vázquez-Lorenzo,et al.  LORENTZIAN 3-MANIFOLDS WITH COMMUTING CURVATURE OPERATORS , 2008 .

[199]  A. Ikemakhen,et al.  Sur l'holonomie des variétés pseudo-riemanniennes de signature (2, 2+n) , 1999 .

[200]  Kouei Sekigawa,et al.  On some 4-dimensional compact Einstein almost Kähler manifolds , 1985 .

[201]  Martin A. Magid SHAPE OPERATORS OF EINSTEIN HYPERSURFACES IN INDEFINITE SPACE FORMS , 1982 .

[202]  Neda Bokan,et al.  On the complete decomposition of curvature tensors of Riemannian manifolds with symmetric connection , 1990 .

[203]  J. Plebański,et al.  The intrinsic spinorial structure of hyperheavens , 1976 .

[204]  Yulian Tsankov,et al.  A characterization of n-dimensional hypersurfaces in $R^{n+1}$ with commuting curvature operators , 2005 .

[205]  Stana Nikcevic,et al.  CURVATURE STRUCTURE OF SELF-DUAL 4-MANIFOLDS , 2008, 0808.2799.

[206]  Yasuo Matsushita Four-dimensional Walker metrics and symplectic structures , 2004 .

[207]  S. A. Robertson,et al.  Parallel framings and foliations on pseudoriemannian manifolds , 1974 .

[208]  I. M. Singer,et al.  Infinitesimally homogeneous spaces , 1960 .

[209]  Ramón Vázquez-Lorenzo,et al.  Four-dimensional Osserman metrics with nondiagonalizable Jacobi operators , 2005 .

[210]  Thomas Mohaupt,et al.  'Special geometry of Euclidean supersymmetry I: Vector multiplets' , 2004 .

[211]  Andrzej Derdzinski,et al.  Walker’s theorem without coordinates , 2006 .

[212]  Giovanni Calvaruso,et al.  Curvature homogeneous Lorentzian three-manifolds , 2009 .

[213]  Peter B. Gilkey Algebraic curvature tensors which are p-Osserman , 2001 .

[214]  P. Gilkey,et al.  The geometry of modified Riemannian extensions , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[215]  Peter R. Law,et al.  Neutral Einstein metrics in four dimensions , 1991 .

[216]  Barbara Opozda Affine Versions of Singer's Theorem on Locally Homogeneous Spaces , 1997 .

[217]  Varun Sahni,et al.  NEW VISTAS IN BRANEWORLD COSMOLOGY , 2002 .