Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues

Conformal Osserman four-dimensional manifolds are studied with special attention to the construction of new examples showing that the algebraic structure of any such curvature tensor can be realized at the differentiable level. As a consequence one gets examples of anti-self-dual manifolds whose anti-self-dual curvature operator has complex eigenvalues.

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

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

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

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

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

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

[7]  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.

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

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

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

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

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

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

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

[15]  H. Kamada,et al.  SELF-DUALITY OF METRICS OF TYPE (2, 2) ON FOUR-DIMENSIONAL MANIFOLDS , 1997 .

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

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

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

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

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

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

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

[23]  ∈. ⊗4V.  THE SPECTRAL GEOMETRY OF THE WEYL CONFORMAL TENSOR , 2005 .

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

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