Differential Geometry and Lie Groups

[1]  Yvette Kosmann-Schwarzbach,et al.  Groups and Symmetries , 2022, Universitext.

[2]  Y. Wong,et al.  Differentiable Manifolds , 2009 .

[3]  Kristopher Tapp,et al.  Matrix Groups for Undergraduates , 2016 .

[4]  Brigitte Maier,et al.  Fundamentals Of Differential Geometry , 2016 .

[5]  Karolin Papst,et al.  Functions Of Mathematical Physics , 2016 .

[6]  F. Catanese.  Topological methods in algebraic geometry , 2015 .

[7]  Marcelo Siqueira,et al.  Parametric pseudo-manifolds , 2012 .

[8]  N. Dragon.  The Geometry of Special Relativity: A Concise Course , 2012 .

[9]  G. Naber,et al.  The Theory of Spinors , 2012 .

[10]  Jean Gallier,et al.  Geometric Methods and Applications , 2011 .

[11]  R. Cooke.  Real and Complex Analysis , 2011 .

[12]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[13]  Y. Kosmann-Schwarzbach.  Groups and Symmetries: From Finite Groups to Lie Groups , 2009 .

[14]  J. Fourier.  Théorie analytique de la chaleur , 2009 .

[15]  Levent Tunçel,et al.  Optimization algorithms on matrix manifolds , 2009, Math. Comput..

[16]  R. Wilson.  The classical groups , 2009 .

[17]  Nicholas Ayache,et al.  A Fast and Log-Euclidean Polyaffine Framework for Locally Linear Registration , 2009, Journal of Mathematical Imaging and Vision.

[18]  J. Gallier.  Logarithms and Square Roots of Real Matrices , 2008, 0805.0245.

[19]  Loring W. Tu,et al.  An introduction to manifolds , 2007 .

[20]  Nicholas Ayache,et al.  Geometric Means in a Novel Vector Space Structure on Symmetric Positive-Definite Matrices , 2007, SIAM J. Matrix Anal. Appl..

[21]  Vincent Arsigny,et al.  Processing Data in Lie Groups : An Algebraic Approach. Application to Non-Linear Registration and Diffusion Tensor MRI. (Traitement de données dans les groupes de Lie : une approche algébrique. Application au recalage non-linéaire et à l'imagerie du tenseur de diffusion) , 2006 .

[22]  A. Fordy.  AN INTRODUCTION TO LIE GROUPS AND THE GEOMETRY OF HOMOGENEOUS SPACES (Student Mathematical Library 22) , 2006 .

[23]  Xavier Pennec,et al.  Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements , 2006, Journal of Mathematical Imaging and Vision.

[24]  Nicholas Ayache,et al.  Polyrigid and polyaffine transformations: A novel geometrical tool to deal with non-rigid deformations - Application to the registration of histological slices , 2005, Medical Image Anal..

[25]  N. Higham.  The Scaling and Squaring Method for the Matrix Exponential Revisited , 2005, SIAM J. Matrix Anal. Appl..

[26]  R. Osserman,et al.  A Panoramic View of Riemannian Geometry. , 2005 .

[27]  M. Marias.  Analysis on Manifolds , 2005 .

[28]  A. Bobenko.  Compact Riemann Surfaces , 2005 .

[29]  B. Hall.  Lie Groups, Lie Algebras, and Representations: An Elementary Introduction , 2004 .

[30]  A. Kirillov.  Lectures on the Orbit Method , 2004 .

[31]  W. Fulton,et al.  Lie Algebras and Lie Groups , 2004 .

[32]  H. O. Erdin.  Characteristic Classes , 2004 .

[33]  Marion Kee,et al.  Analysis , 2004, Machine Translation.

[34]  Andreas Arvanitoyeorgos,et al.  An Introduction to Lie Groups and the Geometry of Homogeneous Spaces , 2003 .

[35]  A. Baker.  Matrix Groups: An Introduction to Lie Group Theory , 2003 .

[36]  Robin Green,et al.  Spherical Harmonic Lighting: The Gritty Details , 2003 .

[37]  John M. Lee.  Introduction to Smooth Manifolds , 2002 .

[38]  W. Rossmann.  Lie Groups: An Introduction through Linear Groups , 2002 .

[39]  A. Deitmar.  A First Course in Harmonic Analysis , 2002 .

[40]  W. Kühnel.  Differential Geometry: Curves - Surfaces - Manifolds , 2002 .

[41]  B. Dundas,et al.  DIFFERENTIAL TOPOLOGY , 2002 .

[42]  A. Blumberg.  BASIC TOPOLOGY , 2002 .

[43]  Kostas Daniilidis,et al.  Catadioptric projective geometry: theory and applications , 2002 .

[44]  Ronen Basri,et al.  Lambertian reflectance and linear subspaces , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[45]  Nicholas J. Higham,et al.  Approximating the Logarithm of a Matrix to Specified Accuracy , 2000, SIAM J. Matrix Anal. Appl..

[46]  森田 茂之,et al.  Geometry of differential forms , 2001 .

[47]  A. Borel.  Essays in the history of Lie groups and algebraic groups , 2001 .

[48]  Ernst Hairer.  Analyse II (Calcul Différentiel et Equations Différentielles) , 1999 .

[49]  W. Hsiang,et al.  Lectures on Lie Groups , 1998 .

[50]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[51]  I. Madsen,et al.  From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes , 1997 .

[52]  S. Rosenberg.  The Laplacian on a Riemannian Manifold: The Laplacian on a Riemannian Manifold , 1997 .

[53]  J. Lafontaine.  Introduction aux variétés différentielles , 2020 .

[54]  S. Chern,et al.  Differential Geometry: Cartan's Generalization of Klein's Erlangen Program , 2000 .

[55]  K. Paranjape.  Geometry VI , 1996 .

[56]  Pierre Cartier,et al.  The algebraic theory of spinors and Clifford algebras , 1996 .

[57]  John F. Hughes,et al.  Modeling surfaces of arbitrary topology using manifolds , 1995, SIGGRAPH.

[58]  I. G. MacDonald,et al.  Lectures on Lie groups and Lie algebras , 1995 .

[59]  G. Folland.  A course in abstract harmonic analysis , 1995 .

[60]  J. Jost.  Riemannian geometry and geometric analysis , 1995 .

[61]  R. Bryant.  An introduction to Lie groups and symplectic geometry , 1995 .

[62]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[63]  S. Yau,et al.  Lectures on Differential Geometry , 1994 .

[64]  E. Folke Bolinder,et al.  Clifford Numbers and Spinors , 1993 .

[65]  Bernard Gostiaux,et al.  Géométrie différentielle : variétés, courbes et surfaces , 1992 .

[66]  Joe Harris,et al.  Representation Theory: A First Course , 1991 .

[67]  W. Massey.  A basic course in algebraic topology , 1991 .

[68]  N. Bourbaki,et al.  Lie Groups and Lie Algebras: Chapters 1-3 , 1989 .

[69]  V. Varadarajan,et al.  An Introduction to Harmonic Analysis on Semisimple Lie Groups , 1989 .

[70]  N. Jacobson,et al.  Basic Algebra II , 1989 .

[71]  A. Laub,et al.  Condition Estimates for Matrix Functions , 1989 .

[72]  A. W. Knapp.  Lie groups beyond an introduction , 1988 .

[73]  Jean-Pierre Serre,et al.  Complex Semisimple Lie Algebras , 1987 .

[74]  D. Sattinger,et al.  Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics , 1986 .

[75]  F. Testard,et al.  Introduction a la théorie des groupes de Lie classiques , 1986 .

[76]  B. Dubrovin,et al.  Modern geometry--methods and applications , 1984 .

[77]  R. Howe.  Very Basic Lie Theory , 1983 .

[78]  B. O'neill.  Semi-Riemannian Geometry With Applications to Relativity , 1983 .

[79]  Mitsuru Nishikawa.  On the exponential map of the group O(p,q)0 , 1983 .

[80]  Loring W. Tu,et al.  Differential forms in algebraic topology , 1982, Graduate texts in mathematics.

[81]  John R. Harper,et al.  Algebraic topology : a first course , 1982 .

[82]  M. Bertin,et al.  Algèbre linéaire et géométrie classique , 1981 .

[83]  D. Djoković.  On the exponential map in classical lie groups , 1980 .

[84]  Raymond O. Wells,et al.  Differential analysis on complex manifolds , 1980 .

[85]  S. Chern.  Complex manifolds without potential theory , 1979 .

[86]  A. Mukherjea,et al.  Real and Functional Analysis , 1978 .

[87]  S. Helgason.  Differential Geometry, Lie Groups, and Symmetric Spaces , 1978 .

[88]  Joe W. Harris,et al.  Principles of Algebraic Geometry , 1978 .

[89]  William S. Massey,et al.  Algebraic Topology: An Introduction , 1977 .

[90]  R. Cushman,et al.  Conjugacy classes in linear groups , 1977 .

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

[92]  W. Boothby.  An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[93]  C. R. DePrima,et al.  The range of A−1A∗ in GL(n,C) , 1974 .

[94]  Spinor representations of the orthogonal groups , 1973 .

[95]  J. Humphreys.  Introduction to Lie Algebras and Representation Theory , 1973 .

[96]  C. H. Edwards.  Advanced calculus of several variables , 1973 .

[97]  E. Stein,et al.  Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .

[98]  F. W. Warner.  Foundations of Differentiable Manifolds and Lie Groups , 1971 .

[99]  R. Carter.  Lie Groups , 1970, Nature.

[100]  J. Milnor.  On isometries of inner product spaces , 1969 .

[101]  H. Samelson.  Notes on Lie algebras , 1969 .

[102]  Michael Francis Atiyah,et al.  Introduction to commutative algebra , 1969 .

[103]  N. Vilenkin.  Special Functions and the Theory of Group Representations , 1968 .

[104]  H. O. Foulkes.  Abstract Algebra , 1967, Nature.

[105]  B. Kolman,et al.  An introduction to lie groups and lie algebras , 1968 .

[106]  J. Milnor.  Topology from the differentiable viewpoint , 1965 .

[107]  H. Cartan,et al.  Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes , 1961 .

[108]  Shin-ichi Matsushita.  Topological Groups , 1952 .

[109]  James E. pLebensohn.  Geometry and the Imagination , 1952 .

[110]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[111]  N. Steenrod.  Topology of Fibre Bundles , 1951 .

[112]  H. T. H. PIAGGIO,et al.  Foundations of Algebraic Geometry , 1948, Nature.

[113]  A. G. Walker.  Theory of Lie Groups , 1947, Nature.

[114]  H. Weyl.  The Classical Groups , 1940 .

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

[116]  P J Fox,et al.  THE FOUNDATIONS OF MECHANICS. , 1918, Science.

[117]  R. Ho.  Algebraic Topology , 2022 .

[118]  Christopher J. BISHOPAbstra,et al.  Orthogonal Functions , 2022 .