Riemannian Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1987
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Traditional point of view: pinched manifolds 147 Almost flat pinching 148 Coarse point of view: compactness theorems of Gromov and Cheeger 149 K. CURVATURE AND REPRESENTATIONS OF THE ORTHOGONAL GROUP Decomposition of the space of curvature tensors 150 Conformally flat manifolds 153 The second Bianchi identity 154 CHAPITRE IV : ANALYSIS ON MANIFOLDS AND THE RICCI CURVATURE A. MANIFOLDS WITH BOUNDARY Definition 155 The Stokes theorem and integration by parts 156 B. BISHOP'S INEQUALITY REVISITED 159 Some commutations formulas Laplacian of the distance function 160 Another proof of Bishop's inequality 161 The Heintze-Karcher inequality 162 C. DIFFERENTIAL FORMS AND COHOMOLOGY The de Rham complex 164 Differential operators and their formal adjoints 165 The Hodge-de Rham theorem 167 A second visit to the Bochner method 168 D. BASIC SPECTRAL GEOMETRY 170 The Laplace operator and the wave equation Statement of the basic results on the spectrum 172 E. SOME EXAMPLES OF SPECTRA 172 Introduction The spectrum of flat tori 174 175 Spectrum of (sn, can) F. THE MINIMAX PRINCIPLE 177 The basic statements VIII G. THE RICCI CURVATURE AND EIGENVALUES ESTIMATES Introduction 181 Bishop's inequality and coarse estimates 181 Some consequences of Bishop's theorem 182 Lower bounds for the first eigenvalue 184 CHAPTER V : RIEMANNIAN SUBMANIFOLDS A. CURVATURE OF SUBMANIFOLDS Introduction 185 Second fundamental form 185 Curvature of hypersurfaces 187 Application to explicit computations of curvature 189 B. CURVATURE AND CONVEXITY 192 The Hadamard theorem C. |
| Beschreibung: | 1 Online-Ressource (XI, 248p) |
| ISBN: | 9783642970269 9783540179238 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-97026-9 |
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Datensatz im Suchindex
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| author | Gallot, Sylvestre |
| author_facet | Gallot, Sylvestre |
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| author_variant | s g sg |
| building | Verbundindex |
| bvnumber | BV042423151 |
| classification_tum | MAT 000 |
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| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-97026-9 |
| format | Electronic eBook |
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| id | DE-604.BV042423151 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642970269 9783540179238 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858568 |
| oclc_num | 863947830 |
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| physical | 1 Online-Ressource (XI, 248p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1987 |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Gallot, Sylvestre Verfasser aut Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine Berlin, Heidelberg Springer Berlin Heidelberg 1987 1 Online-Ressource (XI, 248p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Traditional point of view: pinched manifolds 147 Almost flat pinching 148 Coarse point of view: compactness theorems of Gromov and Cheeger 149 K. CURVATURE AND REPRESENTATIONS OF THE ORTHOGONAL GROUP Decomposition of the space of curvature tensors 150 Conformally flat manifolds 153 The second Bianchi identity 154 CHAPITRE IV : ANALYSIS ON MANIFOLDS AND THE RICCI CURVATURE A. MANIFOLDS WITH BOUNDARY Definition 155 The Stokes theorem and integration by parts 156 B. BISHOP'S INEQUALITY REVISITED 159 Some commutations formulas Laplacian of the distance function 160 Another proof of Bishop's inequality 161 The Heintze-Karcher inequality 162 C. DIFFERENTIAL FORMS AND COHOMOLOGY The de Rham complex 164 Differential operators and their formal adjoints 165 The Hodge-de Rham theorem 167 A second visit to the Bochner method 168 D. BASIC SPECTRAL GEOMETRY 170 The Laplace operator and the wave equation Statement of the basic results on the spectrum 172 E. SOME EXAMPLES OF SPECTRA 172 Introduction The spectrum of flat tori 174 175 Spectrum of (sn, can) F. THE MINIMAX PRINCIPLE 177 The basic statements VIII G. THE RICCI CURVATURE AND EIGENVALUES ESTIMATES Introduction 181 Bishop's inequality and coarse estimates 181 Some consequences of Bishop's theorem 182 Lower bounds for the first eigenvalue 184 CHAPTER V : RIEMANNIAN SUBMANIFOLDS A. CURVATURE OF SUBMANIFOLDS Introduction 185 Second fundamental form 185 Curvature of hypersurfaces 187 Application to explicit computations of curvature 189 B. CURVATURE AND CONVEXITY 192 The Hadamard theorem C. Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s 1\p DE-604 Hulin, Dominique Sonstige oth Lafontaine, Jacques Sonstige oth https://doi.org/10.1007/978-3-642-97026-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gallot, Sylvestre Riemannian Geometry Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4128462-8 |
| title | Riemannian Geometry |
| title_auth | Riemannian Geometry |
| title_exact_search | Riemannian Geometry |
| title_full | Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
| title_fullStr | Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
| title_full_unstemmed | Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
| title_short | Riemannian Geometry |
| title_sort | riemannian geometry |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Mathematical physics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Riemannsche Geometrie |
| url | https://doi.org/10.1007/978-3-642-97026-9 |
| work_keys_str_mv | AT gallotsylvestre riemanniangeometry AT hulindominique riemanniangeometry AT lafontainejacques riemanniangeometry |