Metric rigidity theorems on hermitian locally symmetric manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore u.a.
World Scientific
1989
|
| Series: | Series in pure mathematics
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 278 S. |
| ISBN: | 9971508001 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804118287759441920 |
|---|---|
| adam_text | ix
TABLE OF CONTENTS
PREFACE vii
INTRODUCTION 1
PART I BACKGROUND AND FIRST RESULTS
CHAPTER 1 HISTORICAL BACKGROUND AND
SUMMARY OF RESULTS
§1 Historical Background 9
§2 Statement of Results 13
§3 Deduction of Some Results from the Hermitian Metric Rigidity
Theorem in the Seminegative Case 15
CHAPTER 2 FUNDAMENTALS OF HERMITIAN AND
KA.HLER GEOMETRIES
§1 Hermitian and Kahler Metrics 17
§2 The Hermitian Connection and its Curvature 22
§3 Different Notions of Positivity/Negativity of Curvature 27
§4 Projectivization of Hermitian Holomorphic Line Bundles 34
CHAPTER 3 RIEMANNIAN AND HERMITIAN
SYMMETRIC MANIFOLDS
§ 1 Definition and Basic Properties of Riemannian
Symmetric Manifolds 40
§2 Hermitian Symmetric Manifolds 47
§3 The Borel Embedding Theorem 51
X
CHAPTER 4 BOUNDED SYMMETRIC DOMAINS —
THE CLASSICAL CASES
§1 The Bergman and Caratheodory Metrics on Bounded Domains 55
§2 Classical Bounded Symmetric Domains 61
§3 Curvatures of Classical Bounded Symmetric Domains 80
CHAPTER 5 BOUNDED SYMMETRIC DOMAINS —
GENERAL THEORY
§1 The Polydisc Theorem (and the Polysphere Theorem) 88
§2 The Harish Chandra Embedding Theorem 94
CHAPTER 6 THE HERMITIAN METRIC RIGIDITY
THEOREM FOR COMPACT QUOTIENTS
§1 The Characteristic Bundle S 99
§2 An Integral Formula on S and an Algebraic Deduction of the
Hermitian Metric Rigidity Theorem for Compact Quotients 106
§3 An Alternative Proof Using Moore s Ergodicity Theorem 113
§4 The Case of Irreducible and Locally Reducible
Compact Quotients 117
§5 Applications of the Hermitian Metric Rigidity
Theorem and Its Proofs 122
CHAPTER 7 THE KAHLER METRIC RIGIDITY
THEOREM IN THE SEMIPOSITIVE CASE
§1 Hermitian Symmetric Manifolds of Compact Type 133
§2 The Dual Characteristic Bundle S* and
an Integral Formula 137
§3 The Characteristic Bundle and Minimal Rational Curves 142
§4 Proof of the Metric Rigidity Theorem 147
xi
PART II FURTHER DEVELOPMENT
CHAPTER 8 THE HERMITIAN METRIC RIGIDITY
THEOREM FOR QUOTIENTS OF
FINITE VOLUME
§1 Compactifications of Arithmetic Varieties and
an Integral Formula 159
§2 An Alternative Proof in the Kahler Case 165
CHAPTER 9 THE IMMERSION PROBLEM FOR
COMPLEX HYPERBOLIC SPACE FORMS
§1 The Equi Dimensional Case 173
§2 Holomorphic Immersions Between Compact
Hyperbolic Space Forms 180
CHAPTER 10 THE HERMITIAN METRIC RIGIDITY
THEOREM ON LOCALLY HOMOGENEOUS
HOLOMORPHIC VECTOR BUNDLES
§1 Homogeneous Hermitian Vector Bundles on
Bounded Symmetric Domains 194
§2 An Extension of the Hermitian Metric Rigidity Theorem
and Applications 201
CHAPTER 11 A RIGIDITY THEOREM FOR
HOLOMORPHIC MAPPINGS BETWEEN
IRREDUCIBLE HERMITIAN SYMMETRIC
MANIFOLDS OF COMPACT TYPE
§1 Formulation of the Problem 213
§2 Minimal Rational Curves on Hermitian Symmetric Manifolds
of Compact Type 216
§3 Proof of the Rigidity Theorem for Holomorphic Mappings 219
xii
APPENDIX
I. SEMISIMPLE LIE ALGEBRAS AND THEIR
REPRESENTATIONS
1.1 Semisimple Lie Algebras — General Theorems 227
1.2 Cartan Subalgebras 228
1.3 Semisimple Lie Algebras — Structure Theory 230
1.4 Representations of Semisimple Lie Algebras 233
1.5 Some Results on Lie Groups and Their Representations 237
II. SOME THEOREMS IN RIEMANNIAN GEOMETRY
II. 1 The de Rham Decomposition Theorem 239
II.2 Some Theorems on Riemannian Locally
Symmetric Manifolds 239
III. CHARACTERISTIC PROJECTIVE SUBVARIETIES
ASSOCIATED TO HERMITIAN SYMMETRIC
MAND7OLDS
III. 1 Equivalent Definitions of Characteristic Vectors 242
III.2 Characteristic Projective Subvarieties as Symmetric Projective
Submanifolds with Parallel Second Fundamental Forms 245
III. 3 Enumeration of the Characteristic Projective Subvarieties 249
III.4 Higher Characteristic Bundles 251
IV. A DUAL GENERALIZED FRANKEL CONJECTURE
FOR COMPACT KAHLER MANIFOLDS
OF SEMINEGATIVE BISECTIONAL CURVATURE
IV. 1 Background 254
IV.2 Formulation of a Dual Generalized Frankel Conjecture 256
BD3LIOGRAPHY 265
INDEX 273
|
| any_adam_object | 1 |
| author | Mok, Ngaiming |
| author_facet | Mok, Ngaiming |
| author_role | aut |
| author_sort | Mok, Ngaiming |
| author_variant | n m nm |
| building | Verbundindex |
| bvnumber | BV004057149 |
| classification_rvk | SK 350 SK 780 |
| ctrlnum | (OCoLC)260198221 (DE-599)BVBBV004057149 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004057149 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:07:54Z |
| institution | BVB |
| isbn | 9971508001 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002537205 |
| oclc_num | 260198221 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-706 DE-11 |
| owner_facet | DE-12 DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-706 DE-11 |
| physical | XII, 278 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in pure mathematics |
| series2 | Series in pure mathematics |
| spelling | Mok, Ngaiming Verfasser aut Metric rigidity theorems on hermitian locally symmetric manifolds Singapore u.a. World Scientific 1989 XII, 278 S. txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics 6 Krümmung (DE-588)4128765-4 gnd rswk-swf Lokal symmetrische Mannigfaltigkeit (DE-588)4168099-6 gnd rswk-swf Symmetrischer Raum (DE-588)4184206-6 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Hermitesche Form (DE-588)4159610-9 gnd rswk-swf Lokal symmetrische Mannigfaltigkeit (DE-588)4168099-6 s Krümmung (DE-588)4128765-4 s DE-604 Hermitesche Form (DE-588)4159610-9 s Symmetrischer Raum (DE-588)4184206-6 s Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Series in pure mathematics 6 (DE-604)BV000016845 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002537205&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mok, Ngaiming Metric rigidity theorems on hermitian locally symmetric manifolds Series in pure mathematics Krümmung (DE-588)4128765-4 gnd Lokal symmetrische Mannigfaltigkeit (DE-588)4168099-6 gnd Symmetrischer Raum (DE-588)4184206-6 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Hermitesche Form (DE-588)4159610-9 gnd |
| subject_GND | (DE-588)4128765-4 (DE-588)4168099-6 (DE-588)4184206-6 (DE-588)4031996-9 (DE-588)4159610-9 |
| title | Metric rigidity theorems on hermitian locally symmetric manifolds |
| title_auth | Metric rigidity theorems on hermitian locally symmetric manifolds |
| title_exact_search | Metric rigidity theorems on hermitian locally symmetric manifolds |
| title_full | Metric rigidity theorems on hermitian locally symmetric manifolds |
| title_fullStr | Metric rigidity theorems on hermitian locally symmetric manifolds |
| title_full_unstemmed | Metric rigidity theorems on hermitian locally symmetric manifolds |
| title_short | Metric rigidity theorems on hermitian locally symmetric manifolds |
| title_sort | metric rigidity theorems on hermitian locally symmetric manifolds |
| topic | Krümmung (DE-588)4128765-4 gnd Lokal symmetrische Mannigfaltigkeit (DE-588)4168099-6 gnd Symmetrischer Raum (DE-588)4184206-6 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Hermitesche Form (DE-588)4159610-9 gnd |
| topic_facet | Krümmung Lokal symmetrische Mannigfaltigkeit Symmetrischer Raum Komplexe Mannigfaltigkeit Hermitesche Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002537205&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016845 |
| work_keys_str_mv | AT mokngaiming metricrigiditytheoremsonhermitianlocallysymmetricmanifolds |