Holdings: The geometry of curvature homogeneous pseudo-Riemannian manifolds

The geometry of curvature homogeneous pseudo-Riemannian manifolds:

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Bibliographic Details
Main Author:	Gilkey, Peter B. 1946- (Author)
Format:	Book
Language:	English
Published:	London Imperial College Press 2007
Series:	ICP advanced texts in mathematics 2
Subjects:	Curvature Geometry, Differential Riemannian manifolds Pseudo-Riemannscher Raum
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 376 S.
ISBN:	9781860947858 1860947859

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adam_text	Contents Preface The Geometry of the Riemann Curvature Tensor 1 1.1 Introduction ........................... 1 1.2 Basic Geometrical Notions ................... 4 1.2.1 Vector spaces with symmetric inner products .... 4 1.2.2 Vector bundles, connections, and curvature ..... 6 1.2.3 Holonomy and parallel translation .......... 10 1.2.4 Affine manifolds, geodesies, and completeness .... 11 1.2.5 Pseudo- Riemannian manifolds ............. 12 1.2.6 Scalar Weyl invariants ................. 15 1.3 Algebraic Curvature Tensors and Homogeneity ....... 16 1.3.1 Algebraic curvature tensors .............. 17 1.3.2 Canonical curvature tensors .............. 21 1.3.3 The Weyl conformai curvature tensor ......... 23 1.3.4 Models .......................... 24 1.3.5 Various notions of homogeneity ............ 26 1.3.6 Killing vector fields ................... 27 1.3.7 Nilpotent curvature ................... 28 1.4 Curvature Homogeneity - a Brief Literature Survey ..... 28 1.4.1 Scalar Weyl invariants in the Riemannian setting . . 28 1.4.2 Relating curvature homogeneity and homogeneity . . 29 1.4.3 Manifolds modeled on symmetric spaces ....... 30 1.4.4 Historical survey .................... 31 1.5 Results from Linear Algebra .................. 32 1.5.1 Symmetric and anti-symmetric operators ....... 32 The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds 2. 1.5.2 The spectrum of an operator ............. 32 1.5.3 Jordan normal form .................. 33 1.5.4 Self-adjoint maps in the higher signature setting ... 34 1.5.5 Technical results concerning differential equations . . 35 1.6 Results from Differential Geometry .............. 38 1.6.1 Principle bundles .................... 39 1.6.2 Geometric readability ................. 39 1.6.3 The canonical algebraic curvature tensors ...... 41 1.6.4 Complex geometry ................... 47 1.6.5 Rank l-symmetric spaces ............... 51 1.6.6 Conformai complex space forms ............ 53 1.6.7 Kahler geometry .................... 54 1.7 The Geometry of the Jacobi Operator ............ 54 1.7.1 The Jacobi operator .................. 55 1.7.2 The higher order Jacobi operator ........... 57 1.7.3 The conformai Jacobi operator ............ 59 1.7.4 The complex Jacobi operator ............. 60 1.8 The Geometry of the Curvature Operator .......... 62 1.8.1 The skew-symmetric curvature operator ....... 62 1.8.2 The conformai skew-symmetric curvature operator . 65 1.8.3 The Stanilov operator ................. 66 1.8.4 The complex skew-symmetric curvature operator . . 66 1.8.5 The Szabó operator ................... 68 1.9 Spectral Geometry of the Curvature Tensor ......... 69 1.9.1 Analytic continuation .................. 70 1.9.2 Duality .......................... 72 1.9.3 Bounded spectrum ................... 75 1.9.4 The Jacobi operator .................. 78 1.9.5 The higher order Jacobi operator ........... 81 1.9.6 The conformai and complex Jacobi operators .... 82 1.9.7 The Stanilov and the Szabó operators ........ 83 1.9.8 The skew-symmetric curvature operator ....... 84 1.9.9 The conformai skew-symmetric curvature operator . 86 Curvature Homogeneous Generalized Plane Wave Manifolds 87 2.1 Introduction ........................... 87 2.2 Generalized Plane Wave Manifolds .............. 90 2.2.1 The geodesic structure ................. 92 2.2.2 The curvature tensor .................. 93 Contents 3. 2.2.3 The geometry of the curvature tensor ......... 94 2.2.4 Local scalar invariants ................. 94 2.2.5 Parallel vector fields and holonomy .......... 96 2.2.6 Jacobi vector fields ................... 96 2.2.7 Isometries ........................ 97 2.2.8 Symmetric spaces .................... 99 2.3 Manifolds of Signature (2,2).................. 101 2.3.1 Immersions as hypersurfaces in flat space ....... 103 2.3.2 Spectral properties of the curvature tensor ...... 105 2.3.3 A complete system of invariants ............ 107 2.3.4 Isometries ........................ 109 2.3.5 Estimating кРіЯ if min(p, q) — 2............ 114 2.4 Manifolds of Signature (2,4).................. 115 2.5 Plane Wave Hypersurfaces of Neutral Signature (p,p) . . . 119 2.5.1 Spectral properties of the curvature tensor ...... 123 2.5.2 Curvature homogeneity ................. 128 2.6 Plane Wave Manifolds with Flat Factors ........... 130 2.7 Nikčević Manifolds ....................... 135 2.7.1 The curvature tensor .................. 137 2.7.2 Curvature homogeneity ................. 139 2.7.3 Local isometry invariants ................ 141 2.7.4 The spectral geometry of the curvature tensor .... 145 2.8 Dunn Manifolds ......................... 149 2.8.1 Models and the structure groups ........... 151 2.8.2 Invariants which are not of Weyl type ........ 155 2.9 fc-Curvature Homogeneous Manifolds I ............ 156 2.9.1 Models .......................... 159 2.9.2 Affine invariants ..................... 162 2.9.3 Changing the signature ................. 164 2.9.4 Indecomposability .................... 165 2.10 fc-Curvature Homogeneous Manifolds II ........... 166 2.10.1 Models .......................... 168 2.10.2 Isometry groups ..................... 171 Other Pseudo-Riemannian Manifolds 181 3.1 Introduction ........................... 181 3.2 Lorentz Manifolds ....................... 182 3.2.1 Geodesies and curvature ................ 185 3.2.2 Ricci blowup ...................... 187 The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds 3.2.3 Curvature homogeneity ................. 188 3.3 Signature (2,2) Walker Manifolds ............... 193 3.3.1 Osserman curvature tensors of signature (2,2) .... 194 3.3.2 Indefinite Kahler Osserman manifolds ........ 196 3.3.3 Jordan Osserman manifolds which are not nilpotent 197 3.3.4 Conformally Osserman manifolds ........... 198 3.4 Geodesic Completeness and Ricci Blowup .......... 201 3.4.1 The geodesic equation ................. 201 3.4.2 Conformally Osserman manifolds ........... 202 3.4.3 Jordan Osserman Walker manifolds .......... 206 3.5 Fiedler Manifolds ........................ 206 3.5.1 Geometric properties of Fiedler manifolds ...... 207 3.5.2 Fiedler manifolds of signature (2,2).......... 209 3.5.3 Nilpotent Jacobi manifolds of order 2r ........ 209 3.5.4 Nilpotent Jacobi manifolds of order 2т + 1...... 213 3.5.5 Szabó nilpotent manifolds of arbitrarily high order . 216 4. The Curvature Tensor 219 4.1 Introduction ........................... 219 4.2 Topological Results ....................... 221 4.2.1 Real vector bundles ................... 221 4.2.2 Bundles over projective spaces ............. 222 4.2.3 Clifford algebras in arbitrary signatures ....... 223 4.2.4 Riemannian Clifford algebras ............. 224 4.2.5 Vector fields on spheres ................. 226 4.2.6 Metrics of higher signatures on spheres ........ 226 4.2.7 Equivariant vector fields on spheres .......... 227 4.2.8 Geometrically symmetric vector bundles ....... 228 4.3 Generators for the Spaces Alg0 and ,41g!........... 229 4.3.1 A lower bound for v{m) and for v (m) ........ 231 4.3.2 Geometric realizability . . . . : ............. 233 4.4 Jordan Osserman Algebraic Curvature Tensors ....... 234 4.4.1 Neutral signature Jordan Osserman tensors ..... 235 4.4.2 Rigidity results for Jordan Osserman tensors ..... 238 4.5 The Szabó Operator ...................... 241 4.5.1 Szabó 1-models ..................... 242 4.5.2 Balanced Szabó pseudo-Riemannian manifolds .... 243 4.6 Conformai Geometry ...................... 245 4.6.1 The Weyl model .................... 245 Contents 4.6.2 Conformally Jordan Osserman 0-models ....... 246 4.6.3 Conformally Osserman 4-dimensional manifolds . . . 247 4.6.4 Conformally Jordan Ivanov-Petrova 0-models .... 249 4.7 Stanilov Models ......................... 251 4.8 Complex Geometry ....................... 253 5. Complex Osserman Algebraic Curvature Tensors 257 5.1 Introduction ........................... 257 5.1.1 Clifford families ..................... 257 5.1.2 Complex Osserman tensors .............. 258 5.1.3 Classification results in the algebraic setting ..... 259 5.1.4 Geometric examples .................. 260 5.1.5 Chapter outline ..................... 261 5.2 Technical Preliminaries ..................... 261 5.2.1 Criteria for complex Osserman models ........ 262 5.2.2 Controlling the eigenvalue structure .......... 263 5.2.3 Examples of complex Osserman 0-models ...... 264 5.2.4 Reparametrization of a Clifford family ........ 265 5.2.5 The dual Clifford family ................ 265 5.2.6 Compatible complex models given by Clifford families 266 5.2.7 Linearly independent endomorphisms ......... 269 5.2.8 Technical results concerning Clifford algebras .... 272 5.3 Clifford Families of Rank 1 .................. 276 5.4 Clifford Families of Rank 2 .................. 278 5.4.1 The tensor CxAj, + c2AJs ............... 279 5.4.2 The tensor c0A{.t.) +cxAJl + c2AJs .......... 286 5.5 Clifford Families of Rank 3 .................. 288 5.5.1 Technical results .................... 288 5.5.2 The tensor A = c^Aj, + с2Ајѕ + сгАЈз........ 291 5.5.3 The tensor A = с0А(.г) + ciAj, + c2AJs + сзАј, .. 292 5.6 Tensors A = ciAj, + ... + clAJi for í > 4 .......... 295 5.7 Tensors A = c0A{.t.) -f-ciAj, +... + ciAjt for l> 4..... 301 6. Stanilov-Tsankov Theory 309 6.1 Introduction ........................... 309 6.1.1 Jacobi Tsankov manifolds ............... 310 6.1.2 Skew Tsankov manifolds ................. 311 6.1.3 Stanilov-Videv manifolds ............... 312 xii The Geometry of Curvature Homogeneous Pseudo- Riemannian Manifolds 6.1.4 Jacobi Videv manifolds and 0- models ......... 313 6.2 Riemannian Jacobi Tsankov Manifolds and 0-Models .... 313 6.2.1 Riemannian Jacobi Tsankov 0-models ........ 314 6.2.2 Riemannian orthogonally Jacobi Tsankov 0-models . 315 6.2.3 Riemannian Jacobi Tsankov manifolds ........ 322 6.3 Pseudo-Riemannian Jacobi Tsankov 0-Models ........ 323 6.3.1 Jacobi Tsankov 0-models ................ 324 6.3.2 Non Jacobi Tsankov 0-models with Jl = 0 V χ ... 325 6.3.3 0-models with JxJy =0 Va;, y Є V .......... 326 6.3.4 0-models with AxyAzw = 0 V x,y,z,w Є V ...... 328 6.4 A Jacobi Tsankov О -Model with JxJy φ 0 for some x,y . . 331 6.4.1 The model 9Я14 ..................... 333 6.4.2 A geometric realization of 9Лн ............ 338 6.4.3 Isometry invariants ................... 340 6.4.4 A symmetric space with model ЯЯн ......... 343 6.5 Riemannian Skew Tsankov Models and Manifolds ...... 345 6.5.1 Riemannian skew Tsankov models .......... 347 6.5.2 3-dimensional skew Tsankov manifolds ........ 349 6.5.3 Irreducible 4-dimensional skew Tsankov manifolds . . 351 6.5.4 Flats in a Riemannian skew Tsankov manifold .... 353 6.6 Jacobi Videv Models and Manifolds ............. 356 6.6.1 Equivalent properties characterizing Jacobi Videv models .......................... 357 6.6.2 Decomposing Jacobi Videv models .......... 359 Bibliography 361 Index 373
adam_txt	Contents Preface The Geometry of the Riemann Curvature Tensor 1 1.1 Introduction . 1 1.2 Basic Geometrical Notions . 4 1.2.1 Vector spaces with symmetric inner products . 4 1.2.2 Vector bundles, connections, and curvature . 6 1.2.3 Holonomy and parallel translation . 10 1.2.4 Affine manifolds, geodesies, and completeness . 11 1.2.5 Pseudo- Riemannian manifolds . 12 1.2.6 Scalar Weyl invariants . 15 1.3 Algebraic Curvature Tensors and Homogeneity . 16 1.3.1 Algebraic curvature tensors . 17 1.3.2 Canonical curvature tensors . 21 1.3.3 The Weyl conformai curvature tensor . 23 1.3.4 Models . 24 1.3.5 Various notions of homogeneity . 26 1.3.6 Killing vector fields . 27 1.3.7 Nilpotent curvature . 28 1.4 Curvature Homogeneity - a Brief Literature Survey . 28 1.4.1 Scalar Weyl invariants in the Riemannian setting . . 28 1.4.2 Relating curvature homogeneity and homogeneity . . 29 1.4.3 Manifolds modeled on symmetric spaces . 30 1.4.4 Historical survey . 31 1.5 Results from Linear Algebra . 32 1.5.1 Symmetric and anti-symmetric operators . 32 The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds 2. 1.5.2 The spectrum of an operator . 32 1.5.3 Jordan normal form . 33 1.5.4 Self-adjoint maps in the higher signature setting . 34 1.5.5 Technical results concerning differential equations . . 35 1.6 Results from Differential Geometry . 38 1.6.1 Principle bundles . 39 1.6.2 Geometric readability . 39 1.6.3 The canonical algebraic curvature tensors . 41 1.6.4 Complex geometry . 47 1.6.5 Rank l-symmetric spaces . 51 1.6.6 Conformai complex space forms . 53 1.6.7 Kahler geometry . 54 1.7 The Geometry of the Jacobi Operator . 54 1.7.1 The Jacobi operator . 55 1.7.2 The higher order Jacobi operator . 57 1.7.3 The conformai Jacobi operator . 59 1.7.4 The complex Jacobi operator . 60 1.8 The Geometry of the Curvature Operator . 62 1.8.1 The skew-symmetric curvature operator . 62 1.8.2 The conformai skew-symmetric curvature operator . 65 1.8.3 The Stanilov operator . 66 1.8.4 The complex skew-symmetric curvature operator . . 66 1.8.5 The Szabó operator . 68 1.9 Spectral Geometry of the Curvature Tensor . 69 1.9.1 Analytic continuation . 70 1.9.2 Duality . 72 1.9.3 Bounded spectrum . 75 1.9.4 The Jacobi operator . 78 1.9.5 The higher order Jacobi operator . 81 1.9.6 The conformai and complex Jacobi operators . 82 1.9.7 The Stanilov and the Szabó operators . 83 1.9.8 The skew-symmetric curvature operator . 84 1.9.9 The conformai skew-symmetric curvature operator . 86 Curvature Homogeneous Generalized Plane Wave Manifolds 87 2.1 Introduction . 87 2.2 Generalized Plane Wave Manifolds . 90 2.2.1 The geodesic structure . 92 2.2.2 The curvature tensor . 93 Contents 3. 2.2.3 The geometry of the curvature tensor . 94 2.2.4 Local scalar invariants . 94 2.2.5 Parallel vector fields and holonomy . 96 2.2.6 Jacobi vector fields . 96 2.2.7 Isometries . 97 2.2.8 Symmetric spaces . 99 2.3 Manifolds of Signature (2,2). 101 2.3.1 Immersions as hypersurfaces in flat space . 103 2.3.2 Spectral properties of the curvature tensor . 105 2.3.3 A complete system of invariants . 107 2.3.4 Isometries . 109 2.3.5 Estimating кРіЯ if min(p, q) — 2. 114 2.4 Manifolds of Signature (2,4). 115 2.5 Plane Wave Hypersurfaces of Neutral Signature (p,p) . . . 119 2.5.1 Spectral properties of the curvature tensor . 123 2.5.2 Curvature homogeneity . 128 2.6 Plane Wave Manifolds with Flat Factors . 130 2.7 Nikčević Manifolds . 135 2.7.1 The curvature tensor . 137 2.7.2 Curvature homogeneity . 139 2.7.3 Local isometry invariants . 141 2.7.4 The spectral geometry of the curvature tensor . 145 2.8 Dunn Manifolds . 149 2.8.1 Models and the structure groups . 151 2.8.2 Invariants which are not of Weyl type . 155 2.9 fc-Curvature Homogeneous Manifolds I . 156 2.9.1 Models . 159 2.9.2 Affine invariants . 162 2.9.3 Changing the signature . 164 2.9.4 Indecomposability . 165 2.10 fc-Curvature Homogeneous Manifolds II . 166 2.10.1 Models . 168 2.10.2 Isometry groups . 171 Other Pseudo-Riemannian Manifolds 181 3.1 Introduction . 181 3.2 Lorentz Manifolds . 182 3.2.1 Geodesies and curvature . 185 3.2.2 Ricci blowup . 187 The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds 3.2.3 Curvature homogeneity . 188 3.3 Signature (2,2) Walker Manifolds . 193 3.3.1 Osserman curvature tensors of signature (2,2) . 194 3.3.2 Indefinite Kahler Osserman manifolds . 196 3.3.3 Jordan Osserman manifolds which are not nilpotent 197 3.3.4 Conformally Osserman manifolds . 198 3.4 Geodesic Completeness and Ricci Blowup . 201 3.4.1 The geodesic equation . 201 3.4.2 Conformally Osserman manifolds . 202 3.4.3 Jordan Osserman Walker manifolds . 206 3.5 Fiedler Manifolds . 206 3.5.1 Geometric properties of Fiedler manifolds . 207 3.5.2 Fiedler manifolds of signature (2,2). 209 3.5.3 Nilpotent Jacobi manifolds of order 2r . 209 3.5.4 Nilpotent Jacobi manifolds of order 2т + 1. 213 3.5.5 Szabó nilpotent manifolds of arbitrarily high order . 216 4. The Curvature Tensor 219 4.1 Introduction . 219 4.2 Topological Results . 221 4.2.1 Real vector bundles . 221 4.2.2 Bundles over projective spaces . 222 4.2.3 Clifford algebras in arbitrary signatures . 223 4.2.4 Riemannian Clifford algebras . 224 4.2.5 Vector fields on spheres . 226 4.2.6 Metrics of higher signatures on spheres . 226 4.2.7 Equivariant vector fields on spheres . 227 4.2.8 Geometrically symmetric vector bundles . 228 4.3 Generators for the Spaces Alg0 and ,41g!. 229 4.3.1 A lower bound for v{m) and for v\(m) . 231 4.3.2 Geometric realizability . . . . : . 233 4.4 Jordan Osserman Algebraic Curvature Tensors . 234 4.4.1 Neutral signature Jordan Osserman tensors . 235 4.4.2 Rigidity results for Jordan Osserman tensors . 238 4.5 The Szabó Operator . 241 4.5.1 Szabó 1-models . 242 4.5.2 Balanced Szabó pseudo-Riemannian manifolds . 243 4.6 Conformai Geometry . 245 4.6.1 The Weyl model . 245 Contents 4.6.2 Conformally Jordan Osserman 0-models . 246 4.6.3 Conformally Osserman 4-dimensional manifolds . . . 247 4.6.4 Conformally Jordan Ivanov-Petrova 0-models . 249 4.7 Stanilov Models . 251 4.8 Complex Geometry . 253 5. Complex Osserman Algebraic Curvature Tensors 257 5.1 Introduction . 257 5.1.1 Clifford families . 257 5.1.2 Complex Osserman tensors . 258 5.1.3 Classification results in the algebraic setting . 259 5.1.4 Geometric examples . 260 5.1.5 Chapter outline . 261 5.2 Technical Preliminaries . 261 5.2.1 Criteria for complex Osserman models . 262 5.2.2 Controlling the eigenvalue structure . 263 5.2.3 Examples of complex Osserman 0-models . 264 5.2.4 Reparametrization of a Clifford family . 265 5.2.5 The dual Clifford family . 265 5.2.6 Compatible complex models given by Clifford families 266 5.2.7 Linearly independent endomorphisms . 269 5.2.8 Technical results concerning Clifford algebras . 272 5.3 Clifford Families of Rank 1 . 276 5.4 Clifford Families of Rank 2 . 278 5.4.1 The tensor CxAj, + c2AJs . 279 5.4.2 The tensor c0A{.t.) +cxAJl + c2AJs . 286 5.5 Clifford Families of Rank 3 . 288 5.5.1 Technical results . 288 5.5.2 The tensor A = c^Aj, + с2Ајѕ + сгАЈз. 291 5.5.3 The tensor A = с0А(.г) + ciAj, + c2AJs + сзАј, . 292 5.6 Tensors A = ciAj, + . + clAJi for í > 4 . 295 5.7 Tensors A = c0A{.t.) -f-ciAj, +. + ciAjt for l> 4. 301 6. Stanilov-Tsankov Theory 309 6.1 Introduction . 309 6.1.1 Jacobi Tsankov manifolds . 310 6.1.2 Skew Tsankov manifolds . 311 6.1.3 Stanilov-Videv manifolds . 312 xii The Geometry of Curvature Homogeneous Pseudo- Riemannian Manifolds 6.1.4 Jacobi Videv manifolds and 0- models . 313 6.2 Riemannian Jacobi Tsankov Manifolds and 0-Models . 313 6.2.1 Riemannian Jacobi Tsankov 0-models . 314 6.2.2 Riemannian orthogonally Jacobi Tsankov 0-models . 315 6.2.3 Riemannian Jacobi Tsankov manifolds . 322 6.3 Pseudo-Riemannian Jacobi Tsankov 0-Models . 323 6.3.1 Jacobi Tsankov 0-models . 324 6.3.2 Non Jacobi Tsankov 0-models with Jl = 0 V χ . 325 6.3.3 0-models with JxJy =0 Va;, y Є V . 326 6.3.4 0-models with AxyAzw = 0 V x,y,z,w Є V . 328 6.4 A Jacobi Tsankov О -Model with JxJy φ 0 for some x,y . . 331 6.4.1 The model 9Я14 . 333 6.4.2 A geometric realization of 9Лн . 338 6.4.3 Isometry invariants . 340 6.4.4 A symmetric space with model ЯЯн . 343 6.5 Riemannian Skew Tsankov Models and Manifolds . 345 6.5.1 Riemannian skew Tsankov models . 347 6.5.2 3-dimensional skew Tsankov manifolds . 349 6.5.3 Irreducible 4-dimensional skew Tsankov manifolds . . 351 6.5.4 Flats in a Riemannian skew Tsankov manifold . 353 6.6 Jacobi Videv Models and Manifolds . 356 6.6.1 Equivalent properties characterizing Jacobi Videv models . 357 6.6.2 Decomposing Jacobi Videv models . 359 Bibliography 361 Index 373
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id	DE-604.BV023018342
illustrated	Not Illustrated
index_date	2024-07-02T19:12:04Z
indexdate	2024-07-09T21:09:05Z
institution	BVB
isbn	9781860947858 1860947859
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016222466
oclc_num	141384863
open_access_boolean
owner	DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-824 DE-83
owner_facet	DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-824 DE-83
physical	XII, 376 S.
publishDate	2007
publishDateSearch	2007
publishDateSort	2007
publisher	Imperial College Press
record_format	marc
series	ICP advanced texts in mathematics
series2	ICP advanced texts in mathematics
spelling	Gilkey, Peter B. 1946- Verfasser (DE-588)1024266850 aut The geometry of curvature homogeneous pseudo-Riemannian manifolds Peter B. Gilkey London Imperial College Press 2007 XII, 376 S. txt rdacontent n rdamedia nc rdacarrier ICP advanced texts in mathematics 2 Curvature Geometry, Differential Riemannian manifolds Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd rswk-swf Pseudo-Riemannscher Raum (DE-588)4176163-7 s DE-604 ICP advanced texts in mathematics 2 (DE-604)BV023102173 2 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016222466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Gilkey, Peter B. 1946- The geometry of curvature homogeneous pseudo-Riemannian manifolds ICP advanced texts in mathematics Curvature Geometry, Differential Riemannian manifolds Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd
subject_GND	(DE-588)4176163-7
title	The geometry of curvature homogeneous pseudo-Riemannian manifolds
title_auth	The geometry of curvature homogeneous pseudo-Riemannian manifolds
title_exact_search	The geometry of curvature homogeneous pseudo-Riemannian manifolds
title_exact_search_txtP	The geometry of curvature homogeneous pseudo-Riemannian manifolds
title_full	The geometry of curvature homogeneous pseudo-Riemannian manifolds Peter B. Gilkey
title_fullStr	The geometry of curvature homogeneous pseudo-Riemannian manifolds Peter B. Gilkey
title_full_unstemmed	The geometry of curvature homogeneous pseudo-Riemannian manifolds Peter B. Gilkey
title_short	The geometry of curvature homogeneous pseudo-Riemannian manifolds
title_sort	the geometry of curvature homogeneous pseudo riemannian manifolds
topic	Curvature Geometry, Differential Riemannian manifolds Pseudo-Riemannscher Raum (DE-588)4176163-7 gnd
topic_facet	Curvature Geometry, Differential Riemannian manifolds Pseudo-Riemannscher Raum
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016222466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV023102173
work_keys_str_mv	AT gilkeypeterb thegeometryofcurvaturehomogeneouspseudoriemannianmanifolds

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