Submanifolds and isometric immersions:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Houston, Tex.
Publish or Perish
1990
|
| Series: | Mathematics lecture series
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 173 S. |
| ISBN: | 0914098225 |
Staff View
MARC
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| 264 | 1 | |a Houston, Tex. |b Publish or Perish |c 1990 | |
| 300 | |a VIII, 173 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 The Basic Equations For Submanifolds 1
1.0 Introduction 1
1.1 The Fundamental Theorem for Submanifolds 2
1.2 Minimal and umbilical submanifolds 8
1.3 The Axioms of r planes and r spheres 12
Appendix 14
1.4 Riemannian Vector bundles 14
1.5 Proof of the Fundamental Theorem for Submanifolds . 17
Exercises 19
2 Hypersurfaces 23
2.0 Introduction 23
2.1 The Fundamental Theorem for Hypersurfaces 24
2.2 Convex Euclidean hypersurfaces 27
2.3 The classification of Einstein hypersurfaces 32
Exercises 36
3 Submanifolds with Non positive Curvature 39
3.0 Introduction 39
3.1 The Chern Kuiper Theorem 40
3.2 The Jorge Koutroufiotis Theorem 45
Exercises 51
4 Reduction of Codimension 53
4.0 Intoduction 53
4.1 Basic facts 54
4.2 The parallelism of the first normal space 57
4.3 An application 61
Exercises 62
viii CONTENTS
5 Complete Submanifolds of Constant Sectional Curvature . . 65
5.0 Introduction 65
5.1 Completeness of the relative nullity foliation 66
5.2 Isometric immersions between spaces of constant
curvature 71
Exercises 80
6 The Theory of Flat Bilinear Forms and Isometric Rigidity . 82
6.0 Introduction 82
6.1 Flat bilinear forms 83
6.2 Local isometric rigidity 89
6.3 Global isometric rigidity of hypersurfaces 96
Exercises 101
7 Conformally Flat Submanifolds 106
7.0 Introduction 106
7.1 Characterizations of conformally flat manifolds .... 107
7.2 Conformally flat submanifolds with low codimension . 117
7.3 Conformally flat hypersurfaces 126
Exercises 132
8 Real Kaehler Submanifolds 136
8.0 Introduction 136
8.1 Complete real Kaehler submanifolds 137
8.2 Holomorphicity of Real Kaehler Submanifolds .... 142
Exercises 150
9 Conformal Rigidity of Hypersurfaces 152
9.0 Introduction 152
9.1 Cartan s Conformal Rigidity 152
Exercises 160
Bibliography 161
Index 171
|
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| dewey-full | 516.36 |
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| id | DE-604.BV004440399 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:13:05Z |
| institution | BVB |
| isbn | 0914098225 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002754674 |
| oclc_num | 22619776 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-11 |
| physical | VIII, 173 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Publish or Perish |
| record_format | marc |
| series | Mathematics lecture series |
| series2 | Mathematics lecture series |
| spelling | Submanifolds and isometric immersions Marcos Dajczer ... Houston, Tex. Publish or Perish 1990 VIII, 173 S. txt rdacontent n rdamedia nc rdacarrier Mathematics lecture series 13 Hypersurfaces Immersions (Mathematics) Submanifolds Isometrische Immersion (DE-588)4162534-1 gnd rswk-swf Untermannigfaltigkeit (DE-588)4128503-7 gnd rswk-swf Untermannigfaltigkeit (DE-588)4128503-7 s Isometrische Immersion (DE-588)4162534-1 s DE-604 Dajczer, Marcos Sonstige oth Mathematics lecture series 13 (DE-604)BV001891703 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002754674&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Submanifolds and isometric immersions Mathematics lecture series Hypersurfaces Immersions (Mathematics) Submanifolds Isometrische Immersion (DE-588)4162534-1 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd |
| subject_GND | (DE-588)4162534-1 (DE-588)4128503-7 |
| title | Submanifolds and isometric immersions |
| title_auth | Submanifolds and isometric immersions |
| title_exact_search | Submanifolds and isometric immersions |
| title_full | Submanifolds and isometric immersions Marcos Dajczer ... |
| title_fullStr | Submanifolds and isometric immersions Marcos Dajczer ... |
| title_full_unstemmed | Submanifolds and isometric immersions Marcos Dajczer ... |
| title_short | Submanifolds and isometric immersions |
| title_sort | submanifolds and isometric immersions |
| topic | Hypersurfaces Immersions (Mathematics) Submanifolds Isometrische Immersion (DE-588)4162534-1 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd |
| topic_facet | Hypersurfaces Immersions (Mathematics) Submanifolds Isometrische Immersion Untermannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002754674&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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