Projective differential geometry of submanifolds:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Amsterdam u.a.
North-Holland
1993
|
| Series: | North-Holland mathematical library
49 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 362 S. graph. Darst. |
| ISBN: | 0444897712 |
Staff View
MARC
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| 245 | 1 | 0 | |a Projective differential geometry of submanifolds |c M. A. Akivis ; V. V. Goldberg |
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 1993 | |
| 300 | |a XI, 362 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | ix
Table of Contents
Preface v
CHAPTER 1
Preliminaries
1.1 Vector Spaces 1
1.2 Differentiable Manifolds 5
1.3 Projective Space 17
1.4 Some Algebraic Manifolds 26
Notes 31
CHAPTER 2
The Foundations of Projective Differential Geometry of
Submanifolds
2.1 Submanifolds in a Projective Space and Their Tangent
Subspaces 33
2.2 The Second Fundamental Form of a Submanifold 38
2.3 Osculating Subspaces and Fundamental Forms of
Higher Orders of a Submanifold 42
2.4 Asymptotic and Conjugate Directions of Different Orders
on a Submanifold 47
2.5 Some Particular Cases and Examples 53
2.6 Classification of Points of Submanifolds by Means
of the Second Fundamental Form 61
Notes 70
CHAPTER 3
Submanifolds Carrying a Net of Conjugate Lines
3.1 Basic Equations and General Properties 73
3.2 The Holonomicity of the Conjugate Net E2 76
3.3 Classification of Conjugate Nets £2 81
3.4 Some Existence Theorems 85
3.5 The Laplace Transforms of Conjugate Nets and Their
Generalizations 90
3.6 Conic m Conjugate Systems 103
Notes Ill
x Table of Contents
CHAPTER 4
Tangentially Degenerate Submanifolds
4.1 Basic Notions and Equations 113
4.2 Focal Images 117
4.3 Decomposition of Focal Images 120
4.4 The Holonomicity of the Focal Net 122
4.5 Some Other Classes of Tangentially Degenerate
Submanifolds 126
4.6 Manifolds of Hypercones 130
4.7 Parabolic Submanifolds without Singularities in
Euclidean and Non Euclidean Spaces 132
Notes 141
CHAPTER 5
Submanifolds with Asymptotic and Conjugate Distributions
5.1 Distributions on Submanifolds of a Projective Space 143
5.2 Asymptotic Distributions on Submanifolds 145
5.3 Submanifolds with a Complete System of Asymptotic
Distributions 148
5.4 Three Dimensional Submanifolds Carrying a Net of
Asymptotic Lines 151
5.5 Submanifolds with a Complete System of Conjugate
Distributions 165
Notes 171
CHAPTER 6
Normalized Submanifolds in a Projective Space
6.1 The Problem of Normalization of a Submanifold in a
Projective Space 173
6.2 The Affine Connection on a Normalized Submanifold 178
6.3 The Connection in the Normal Bundle 182
6.4 Submanifolds with a Flat Normal Connection 188
6.5 Intrinsic Normalization of Submanifolds 192
6.6 Normalization of Submanifolds Carrying a Conjugate Net
of Lines 199
Notes 205
Table of Contents xi
CHAPTER 7
Projective Differential Geometry of Hypersurfaces
7.1 Basic Equations of the Theory of Hypersurfaces 209
7.2 Osculating Hyperquadrics of a Hypersurface 216
7.3 Invariant Normalizations of a Hypersurface 222
7.4 The Rigidity Problem in a Projective Space 234
7.5 The Geometry of a Surface in Three Dimensional
Projective Space 245
7.6 The Geometry of Hyperbands 255
Notes 266
CHAPTER 8
Algebraization Problems in Projective Differential Geometry
8.1 The First Generalization of Reiss Theorem 271
8.2 The Second Generalization of Reiss Theorem 277
8.3 Degenerate Monge s Varieties 279
8.4 Submanifolds with Degenerate Bisecant Varieties 285
Notes 295
Bibliography 297
Symbols Frequently Used 333
Index 335
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:15:59Z |
| institution | BVB |
| isbn | 0444897712 |
| language | Undetermined |
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| physical | XI, 362 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Akivis, Maks A. 1923- Verfasser (DE-588)128639601 aut Projective differential geometry of submanifolds M. A. Akivis ; V. V. Goldberg Amsterdam u.a. North-Holland 1993 XI, 362 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 49 Projektive Differentialgeometrie (DE-588)4175883-3 gnd rswk-swf Untermannigfaltigkeit (DE-588)4128503-7 gnd rswk-swf Projektive Differentialgeometrie (DE-588)4175883-3 s Untermannigfaltigkeit (DE-588)4128503-7 s DE-604 Golʹdberg, Vladislav V. 1936- Verfasser (DE-588)128639644 aut North-Holland mathematical library 49 (DE-604)BV000005206 49 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005402517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Akivis, Maks A. 1923- Golʹdberg, Vladislav V. 1936- Projective differential geometry of submanifolds North-Holland mathematical library Projektive Differentialgeometrie (DE-588)4175883-3 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd |
| subject_GND | (DE-588)4175883-3 (DE-588)4128503-7 |
| title | Projective differential geometry of submanifolds |
| title_auth | Projective differential geometry of submanifolds |
| title_exact_search | Projective differential geometry of submanifolds |
| title_full | Projective differential geometry of submanifolds M. A. Akivis ; V. V. Goldberg |
| title_fullStr | Projective differential geometry of submanifolds M. A. Akivis ; V. V. Goldberg |
| title_full_unstemmed | Projective differential geometry of submanifolds M. A. Akivis ; V. V. Goldberg |
| title_short | Projective differential geometry of submanifolds |
| title_sort | projective differential geometry of submanifolds |
| topic | Projektive Differentialgeometrie (DE-588)4175883-3 gnd Untermannigfaltigkeit (DE-588)4128503-7 gnd |
| topic_facet | Projektive Differentialgeometrie Untermannigfaltigkeit |
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