Almost complex and complex structures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1995
|
| Series: | Series in pure mathematics
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 310 S. |
| ISBN: | 9810217129 |
Staff View
MARC
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| 245 | 1 | 0 | |a Almost complex and complex structures |c C. C. Hsiung |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1995 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
I. Riemannian Structures 1
1. Manifolds and Structures 1
2. Compactness and Paracompactness 4
3. Partitions of Unity 4
4. Distributions 5
5. Orientability 5
6. Scalars, Vectors and Tensors 6
7. Riemannian Metrics 9
8. Angle of Two Vectors and the Volume Element 11
9. Covariant Differentiation and Geodesies 13
10. Curvature Tensors and Identities 21
11. Sectional Curvature 25
12. Parallel Displacement 30
13. Differential Forms 31
14. Harmonic Forms 41
15. Killing Tensor Fields 43
16. Theorems 48
II. Almost Complex Structures 55
1. Definitions 55
2. Example 56
3. Complexification 60
vii
viii Contents
4. Conditions 61
5. Classifications 67
III. Almost Hermitian Structures 75
1. Almost Hermitian Structures 75
2. Almost Semi Kahlerian Structures 79
3. Quasi Kahlerian Structures 82
4. Almost Kahlerian Structures 83
5. Nearly Kahlerian Structures 85
6. Kahlerian Structures 87
7. Almost L Structures 90
8. Almost Hermitian C Structures 94
9. General Sectional Curvatures 95
10. Holomorphic Sectional Curvatures 97
10.1. Almost complex manifolds 97
10.2. Almost L manifolds 101
10.3. Almost Hermitian C manifolds 105
10.4. Almost Hermitian manifolds 112
10.5. AH3 manifolds 114
11. Holomorphic Bisectional Curvatures 119
12. The Relationship Among the Three Types of
Sectional Curvatures 124
IV. The Real Laplacian 133
1. Commutativity 133
2. The Spectral Geometry 136
2.1. Spectrum 137
2.2. The Minakshisundaram Pleijel
Gaffney s formula 140
2.3. Isospectral Riemannian manifolds 142
2.4. Isospectral almost L manifolds 166
2.5. Isospectral AH2,4 manifolds 176
Contents ix
V. Complex Laplacians 189
1. Complex Operators 189
2. Relations Among Real and Complex Operators 196
3. Complex Laplacians 207
3.1. Laplacian D2 207
3.2. Laplacian Di 214
3.3. Laplacian D3 223
3.4. Laplacian D4 224
3.5. Laplacian D5 226
4. Relationships Among the D s 229
VI. Complex Structures 233
1. Definitions 234
2. Examples 238
3. Relations to Almost Complex Structures 241
4. Integrability of an Almost Complex Structure 243
5. Calculation of d on 0 , 1 and 2 forms 255
6. Theorem and Corollaries 263
VII. Vanishing Theorems 267
1. Maximum Modular Principle and its Applications 267
2. Manifolds with Boundary 273
3. Killing Tensor Fields 279
4. Kahlerian Manifolds 282
Bibliography 285
Index 301
|
| any_adam_object | 1 |
| author | Hsiung, Chuan-Chih 1916-2009 |
| author_GND | (DE-588)1024067696 |
| author_facet | Hsiung, Chuan-Chih 1916-2009 |
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| id | DE-604.BV010774825 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:58:39Z |
| institution | BVB |
| isbn | 9810217129 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007195863 |
| oclc_num | 260203102 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-12 DE-384 DE-703 DE-634 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-12 DE-384 DE-703 DE-634 DE-11 |
| physical | XV, 310 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in pure mathematics |
| series2 | Series in pure mathematics |
| spelling | Hsiung, Chuan-Chih 1916-2009 Verfasser (DE-588)1024067696 aut Almost complex and complex structures C. C. Hsiung Singapore [u.a.] World Scientific 1995 XV, 310 S. txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics 20 Hermitescher Raum (DE-588)4159618-3 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 s DE-604 Riemannscher Raum (DE-588)4128295-4 s Hermitescher Raum (DE-588)4159618-3 s Series in pure mathematics 20 (DE-604)BV000016845 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007195863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsiung, Chuan-Chih 1916-2009 Almost complex and complex structures Series in pure mathematics Hermitescher Raum (DE-588)4159618-3 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4159618-3 (DE-588)4031996-9 (DE-588)4128295-4 |
| title | Almost complex and complex structures |
| title_auth | Almost complex and complex structures |
| title_exact_search | Almost complex and complex structures |
| title_full | Almost complex and complex structures C. C. Hsiung |
| title_fullStr | Almost complex and complex structures C. C. Hsiung |
| title_full_unstemmed | Almost complex and complex structures C. C. Hsiung |
| title_short | Almost complex and complex structures |
| title_sort | almost complex and complex structures |
| topic | Hermitescher Raum (DE-588)4159618-3 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Hermitescher Raum Komplexe Mannigfaltigkeit Riemannscher Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007195863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016845 |
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