Integral formulas in Riemannian geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Dekker
1970
|
| Schriftenreihe: | Pure and applied mathematics
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX,156 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Integral formulas in Riemannian geometry |c Kentarō Yano |
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| 300 | |a IX,156 S. | ||
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| 490 | 1 | |a Pure and applied mathematics |v 1 | |
| 650 | 4 | |a Intégrales | |
| 650 | 4 | |a Riemann, Géométrie de | |
| 650 | 4 | |a Riemann, Variétés de | |
| 650 | 4 | |a Geometry, Riemannian | |
| 650 | 4 | |a Integrals | |
| 650 | 4 | |a Riemannian manifolds | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface v
Chapter 1 Fundamental Concepts and Formulas in
Riemannian Geometry 1
1. Riemannian Manifolds 1
2. Covariant Differentiation 6
3. Curvature Tensor 11
4. Projective and Conformal Transformations 16
5. Lie Derivatives 21
6. Complete Riemannian Manifolds 26
Problems 29
Chapter 2 Harmonic 1 Forms and Killing Vector Fields 38
1. Integral Formulas 38
2. Harmonic 1 Forms 41
3. Killing Vector Fields 43
4. Affine Killing Vector Fields 44
5. Projective Killing Vector Fields 45
6. Conformal Killing Vector Fields 46
Problems 47
vii
Viii CONTENTS
Chapter 3 Riemannian Manifolds Admitting an Infinitesimal
Conformal Transformation 49
1. Preliminaries 49
2. Lemmas 51
3. Integral Formulas 52
4. Theorems on Riemannian Manifolds with Constant Scalar
Curvature and Admitting an Infinitesimal Nonisometric
Conformal Transformation 54
Problems 60
Chapter 4 Harmonic Forms and Killing Tensor Fields 63
1. Harmonic/j Forms 63
2. Killing Tensor Fields 68
3. Curvature and Betti Numbers 70
4. Curvature and Killing Tensor Fields 73
Problems 75
Chapter 5 Hypersurfaces of Riemannian Manifolds 78
1. Fundamental Formulas for Hypersurfaces of a Euclidean Space 78
2. Integral Formulas for Hypersurfaces of a Euclidean Space 82
3. Hypersurfaces of Riemannian Manifolds 87
4. The Induced Connection 89
5. Equations of Gauss and Weingarten 91
6. Equations of Gauss and Codazzi 94
Problems 97
Chapter 6 Closed Hypersurfaces of a Riemannian Manifold
with Constant Mean Curvature 100
1. Hypersurfaces of a Riemannian Manifold Admitting an Infinitesimal
Conformal Transformation 100
2. Integral Formulas 101
3. Integral Formulas for the Case Mt = const 104
4. Hypersurfaces With Constant First Mean Curvature of a Riemannian
Manifold Admitting an Infinitesimal Homothetic Transformation 105
5. Integral Formulas in M Admitting a Function v Such That V V« =
f(p)g 107
6. Hypersurfaces with Constant First Mean Curvature 109
Problems 112
CONTENTS IX
Chapter 7 Harmonic 1 Forms and Killing Vector Fields in
Riemannian Manifolds with Boundary 113
1. Harmonic 1 Forms in Riemannian Manifolds with Boundary 113
2. Killing Vector Fields in Riemannian Manifolds with Boundary 118
3. Conformal Killing Vector Fields in Riemannian Manifolds with
Boundary 120
Problems 124
Chapter 8 Harmonic Forms and Killing Tensor Fields in
Riemannian Manifolds with Boundary 126
1. Tangential and Normal Components of a/ form on the Boundary 126
2. Harmonic/( forms in Riemannian Manifolds with Boundary 129
3. Nonexistence of Harmonic ^ forms 131
4. Killing Forms in Riemannian Manifolds with Boundary 134
5. Nonexistence of Killing/» forms 136
Problems 138
Bibliography 140
Author Index 151
Subject Index 154
|
| any_adam_object | 1 |
| author | Yano, Kentarō 1912-1993 |
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| dewey-full | 516/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.7 |
| dewey-search | 516/.7 |
| dewey-sort | 3516 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002959117 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:25Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001852568 |
| oclc_num | 100478 |
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| physical | IX,156 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Yano, Kentarō 1912-1993 Verfasser (DE-588)119350262 aut Integral formulas in Riemannian geometry Kentarō Yano New York Dekker 1970 IX,156 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 1 Intégrales Riemann, Géométrie de Riemann, Variétés de Geometry, Riemannian Integrals Riemannian manifolds Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Integralformel (DE-588)4161910-9 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Integralformel (DE-588)4161910-9 s DE-604 Differentialgeometrie (DE-588)4012248-7 s Pure and applied mathematics 1 (DE-604)BV000001885 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001852568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yano, Kentarō 1912-1993 Integral formulas in Riemannian geometry Pure and applied mathematics Intégrales Riemann, Géométrie de Riemann, Variétés de Geometry, Riemannian Integrals Riemannian manifolds Differentialgeometrie (DE-588)4012248-7 gnd Integralformel (DE-588)4161910-9 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4161910-9 (DE-588)4128462-8 |
| title | Integral formulas in Riemannian geometry |
| title_auth | Integral formulas in Riemannian geometry |
| title_exact_search | Integral formulas in Riemannian geometry |
| title_full | Integral formulas in Riemannian geometry Kentarō Yano |
| title_fullStr | Integral formulas in Riemannian geometry Kentarō Yano |
| title_full_unstemmed | Integral formulas in Riemannian geometry Kentarō Yano |
| title_short | Integral formulas in Riemannian geometry |
| title_sort | integral formulas in riemannian geometry |
| topic | Intégrales Riemann, Géométrie de Riemann, Variétés de Geometry, Riemannian Integrals Riemannian manifolds Differentialgeometrie (DE-588)4012248-7 gnd Integralformel (DE-588)4161910-9 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Intégrales Riemann, Géométrie de Riemann, Variétés de Geometry, Riemannian Integrals Riemannian manifolds Differentialgeometrie Integralformel Riemannsche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001852568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT yanokentaro integralformulasinriemanniangeometry |