Total mean curvature and submanifolds of finite type:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
1984
|
| Schriftenreihe: | Series in pure mathematics
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 352 S. |
| ISBN: | 9971966026 9971966034 |
Internformat
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| 245 | 1 | 0 | |a Total mean curvature and submanifolds of finite type |c Bang-yen Chen |
| 264 | 1 | |a Singapore |b World Scientific |c 1984 | |
| 300 | |a XI, 352 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Series in pure mathematics |v 1 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface vii
Chapter 1. DIFFERENTIABLE MANIFOLDS
§1. Tensors 1
§2. Tensor Algebras 5
§3. Exterior Algebras 7
§4. Differentiable manifolds 11
§5. Vector Fields and Differential Forms 15
§6. Sard s Theorem and Morse s Inequalities 20
§7. Fibre Bundles 23
§8. Integration of Differential Forms 28
§9. Homology, Cohomology and deRham s Theorem 37
§10. Frobenius Theorem 42
Chapter 2. RIEMANNIAN MANIFOLDS
il. Affine Connections 46
§2. Pseudo Riemannian Manifolds 53
§3. Riemannian Manifolds 56
§4. Exponential Map and Normal Coordinates 62
§5. Weyl Conformal Curvature Tensor 64
§6. Kaehler Manifolds and Quaternionic
Kaehler Manifolds 67
§7. Submersions and Projective Spaces 71
Chapter 3. HODGE THEORY AND SPECTRAL GEOMETRY
51. Operators *, 6 and A 78
§2. Elliptic Differential Operators 85
§3. Hodge deRham Decomposition 91
§4. Heat Equation and its Fundamental Solution 95
§5. Spectra of Some Important Riemannian
Manifolds 100
x Contents
Chapter 4. SUBMANIFOLDS
§ 1. Induced Connections and Second Fundamental
Form 109
§2. Fundamental Equations and Fundamental
Theorems 116
§3. Submanifolds with Flat Normal Connection 124
§4. Totally Umbilical Submanifolds 128
§5. Minimal Submanifolds 135
§6. The First Standard Imbeddings of
Projective Spaces 141
§7. Total Absolute Curvature of Chern and
Lashof 157
§8. Riemannian Submersions 167
59. Submanifolds of Kaehler Manifolds 171
Chapter 5. TOTAL MEAN CURVATURE
Si. Some Results Concerning Surfaces in ]R 182
§2. Total Mean Curvature 187
§3. Conformal Invariants 203
§4. A Variational Problem Concerning Total
Mean Curvature 213
§5. Surfaces in JR. which are Conformally
Equivalent to a Flat Surface 226
§6. Surfaces in ]R4 236
§7. Surfaces in Real Space Forms 244
Chapter 6. SUBMANIFOLDS OF FINITE TYPE
SI. Order of Submanifolds 249
§2. Submanifolds of Finite Type 255
§3. Examples of 2 type Submanifolds 260
§4. Characterizations of 2 type Submanifolds 269
§5. Closed Curves of Finite Type 283
56. Order and Total Mean Curvature 293
57. Some Related Inequalities 300
§8. Some Applications to Spectral Geometry 303
Contents xi
§9. Spectra of Submanifolds of Rank one
Symmetric Spaces 307
§10. Mass symmetric Submanifolds 320
Bibliography 325
Author Index 341
Subject Index 347
|
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| id | DE-604.BV000306770 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:12:01Z |
| institution | BVB |
| isbn | 9971966026 9971966034 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000187406 |
| oclc_num | 260163373 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-706 DE-83 DE-11 DE-188 |
| physical | XI, 352 S. |
| psigel | TUB-www |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in pure mathematics |
| series2 | Series in pure mathematics |
| spelling | Chen, Bang-Yen 1943- Verfasser (DE-588)1022163590 aut Total mean curvature and submanifolds of finite type Bang-yen Chen Singapore World Scientific 1984 XI, 352 S. txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics 1 Mittlere Krümmung (DE-588)4235959-4 gnd rswk-swf Untermannigfaltigkeit (DE-588)4128503-7 gnd rswk-swf Totale kleinste Krümmung (DE-588)4606711-5 gnd rswk-swf Mittlere Krümmung (DE-588)4235959-4 s Untermannigfaltigkeit (DE-588)4128503-7 s DE-604 Totale kleinste Krümmung (DE-588)4606711-5 s Series in pure mathematics 1 (DE-604)BV000016845 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000187406&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Bang-Yen 1943- Total mean curvature and submanifolds of finite type Series in pure mathematics Mittlere Krümmung (DE-588)4235959-4 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd Totale kleinste Krümmung (DE-588)4606711-5 gnd |
| subject_GND | (DE-588)4235959-4 (DE-588)4128503-7 (DE-588)4606711-5 |
| title | Total mean curvature and submanifolds of finite type |
| title_auth | Total mean curvature and submanifolds of finite type |
| title_exact_search | Total mean curvature and submanifolds of finite type |
| title_full | Total mean curvature and submanifolds of finite type Bang-yen Chen |
| title_fullStr | Total mean curvature and submanifolds of finite type Bang-yen Chen |
| title_full_unstemmed | Total mean curvature and submanifolds of finite type Bang-yen Chen |
| title_short | Total mean curvature and submanifolds of finite type |
| title_sort | total mean curvature and submanifolds of finite type |
| topic | Mittlere Krümmung (DE-588)4235959-4 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd Totale kleinste Krümmung (DE-588)4606711-5 gnd |
| topic_facet | Mittlere Krümmung Untermannigfaltigkeit Totale kleinste Krümmung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000187406&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT chenbangyen totalmeancurvatureandsubmanifoldsoffinitetype |