Riemannian manifolds of conullity two:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 300 S. |
| ISBN: | 981022768X |
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MARC
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Record in the Search Index
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| adam_text | RIEMANNIAN MANIFOLDS OF CONULLITYTWO ERIC BOECKX KATHOLIEKE UNIVERSITEIT
LEUVEN, BELGIUM OLDRICH KOWALSKI CHARLES UNIVERSITY, CZECH REPUBLIC
LIEVEN VANHECKE KATHOLIEKE UNIVERSITEIT LEUVEN, BELGIUM WORLD SCIENTIFIC
SINGAPORE »NEW JERSEY *LONDORR HONG KONG CONTENTS INTRODUCTION XI 1
DEFINITION OF SEMI-SYMMETRIC SPACES AND EARLY DEVELOPMENT 1 1.1
NOTATIONAL CONVENTIONS 1 1.2 THE RIEMANN CURVATURE TENSOR AS EQUIVARIANT
MAP ... 2 1.3 DEFINITION OF A SEMI-SYMMETRIC SPACE 4 1.4 THE EXTRINSIC
ANALOGUE: SYMMETRIC AND SEMI-PARALLEL SUBMANIFOLDS 5 1.5 EARLY
DEVELOPMENT 7 2 LOCAL STRUCTURE OF SEMI-SYMMETRIC SPACES 11 2.1 THE
LOCAL STRUCTURE THEOREM 11 2.2 SEMI-SYMMETRIC CONES 16 2.2.1 THE REAL
CONES . , 17 2.2.2 THE KAHLERIAN CONES 19 2.3 RIEMANNIAN MANIFOLDS OF
CONULLITY TWO 19 3 EXPLICIT TREATMENT OF FOLIATED SEMI-SYMMETRIC SPACES
23 3.1 A CANONICAL FORM FOR THE METRICS AND THE BASIC SYSTEM OF PARTIAL
DIFFERENTIAL EQUATIONS 23 3.2 FIRST INTEGRALS 32 3.3 TWO POSSIBLE
SIMPLIFICATIONS 34 3.3.1 A 2 HAS A SPECIAL FORM 34 3.3.2 THE FUNCTIONS G
Q ARE IDENTICALLY ZERO 38 VI CONTENTS 4 CURVATURE HOMOGENEOUS
SEMI-SYMMETRIC SPACES 43 4.1 CURVATURE HOMOGENEOUS SPACES 43 4.2
SEMI-SYMMETRIC CURVATURE HOMOGENEOUS SPACES 45 4.2.1 CONDITIONS FOR
LOCAL SYMMETRY 45 4.2.2 LOCAL STRUCTURE 48 4.2.3 SEKIGAWA S EXAMPLE AND
ITS EXTENSIONS . . . . . . 51 4.3 COMPLETE LOCAL CLASSIFICATION 54 4.3.1
TECHNICAL APPARATUS 54 4.3.2 THE GERMS OF METRICS 60 4.4 AN EXTENSION :
SPACES WITH CONSTANT SCALAR CURVATURE ALONG THE LEAVES 65 4.5 AN
APPLICATION: EINSTEIN-LIKE SEMI-SYMMETRIC SPACES . . 67 5 ASYMPTOTIC
FOLIATIONS AND ALGEBRAIC RANK 73 5.1 ASYMPTOTIC FOLIATIONS ; . . . 73
5.2 ALGEBRAIC RANK 80 6 THREE-DIMENSIONAL RIEMANNIAN MANIFOLDS OF
CONULLITY TWO 85 6.1 THREE-DIMENSIONAL FOLIATED SEMI-SYMMETRIC SPACES
... 85 6.2 RIEMANNIAN INVARIANTS AND ISOMETRIES 88 6.3 CLASSIFICATION OF
THREE-DIMENSIONAL ASYMPTOTICALLY FOLIATED SEMI-SYMMETRIC SPACES 92 6.3.1
PLANARLY FOLIATED SEMI-SYMMETRIC SPACES 92 6.3.2 PARABOLICALLY FOLIATED
SEMI-SYMMETRIC SPACES . . 94 6.3.3 ORTHOGONALLY HYPERBOLICALLY FOLIATED
SEMI-SYMMETRIC SPACES 100 6.3.4 NON-ORTHOGONALLY HYPERBOLICALLY FOLIATED
SEMI-SYMMETRIC SPACES 103 7 ASYMPTOTICALLY FOLIATED SEMI-SYMMETRIC
SPACES 109 7.1 CLASSIFICATION OF ASYMPTOTICALLY FOLIATED SEMI-SYMMETRIC
SPACES WITH ALGEBRAIC RANK ONE 110 7.1.1 PLANARLY FOLIATED
SEMI-SYMMETRIC SPACES 110 7.1.2 PARABOLICALLY FOLIATED SEMI-SYMMETRIC
SPACES . .111 7.1.3 ORTHOGONALLY HYPERBOLICALLY FOLIATED SEMI-SYMMETRIC
SPACES 115 CONTENTS VII 7.1.4 NON-ORTHOGONALLY HYPERBOLICALLY FOLIATED
SEMI-SYMMETRIC SPACES 119 7.2 EXAMPLES OF ASYMPTOTICALLY FOLIATED SPACES
WITH HIGHER ALGEBRAIC RANK 125 7.2.1 HYPERBOLICALLY FOLIATED
SEMI-SYMMETRIC SPACES WITH ALGEBRAIC RANK TWO 125 7.2.2 PARABOLICALLY
FOLIATED SEMI-SYMMETRIC SPACES WITH ALGEBRAIC RANK TWO 127 7.2.3
PARABOLICALLY FOLIATED SEMI-SYMMETRIC SPACES WITH ALGEBRAIC RANK THREE
128 7.3 AN APPLICATION: SEMI-SYMMETRIC 8 ELLIPTIC SEMI-SYMMETRIC SPACES
137 8.1 GENERAL CONSTRUCTION FOR ELLIPTIC SEMI-SYMMETRIC SPACES WITH
ALGEBRAIC RANK ONE 137 8.2 EXAMPLES OF ELLIPTIC SEMI-SYMMETRIC SPACES
WITH HIGHER ALGEBRAIC RANK 144 8.2.1 ELLIPTIC SEMI-SYMMETRIC SPACES WITH
ALGEBRAIC RANK EQUAL TO TWO OR THREE 145 8.2.2 ELLIPTIC SEMI-SYMMETRIC
SPACES WITH ALGEBRAIC RANK EQUAL TO TWO, THREE OR FOUR 151 9 COMPLETE
FOLIATED SEMI-SYMMETRIC SPACES 159 9.1 THREE DIFFERENT CLASSES OF
COMPLETE FOLIATED SEMI-SYMMETRIC SPACES . ; 159 9.2 SEMI-SYMMETRIC
SPACES OF HYPERBOLIC TYPE (IN THE SENSE OF SZABO) 162 9.2.1 COMPLETE
SEMI-SYMMETRIC HYPERSURFACES IN EUCLIDEAN SPACES 163 9.2.2 SZABO S
CONSTRUCTION FOR COMPLETE SEMI- SYMMETRIC HYPERSURFACES OF HYPERBOLIC
TYPE . . . 166 9.2.3 NEW EXAMPLES 170 9.3 SEMI-SYMMETRIC SPACES OF
PARABOLIC TYPE (IN THE SENSE OF SZABO) . . . 175 9.4 THE RELATION
BETWEEN THE TWO TERMINOLOGIES 177 VIII CONTENTS 10 APPLICATION : LOCAL
RIGIDITY PROBLEMS FOR HYPERSURFACES WITH TYPE NUMBER TWO IN JR 4 181
10.1 HYPERSURFACES OF EUCLIDEAN SPACES 182 10.2 THE BASIC SYSTEM OF
PARTIAL DIFFERENTIAL EQUATIONS .... 185 10.3 THREE-DIMENSIONAL FOLIATED
SEMI-SYMMETRIC SPACES AS HYPERSURFACES IN 1R 4 188 10.3.1 PLANARLY
FOLIATED SEMI-SYMMETRIC SPACES 188 10.3.2 PARABOLICALLY FOLIATED
SEMI-SYMMETRIC SPACES . . 190 10.3.3 ORTHOGONALLY HYPERBOLICALLY
FOLIATED SEMI-SYMMETRIC SPACES 198 10.4 RULED HYPERSURFACES IN JR 4 207
11 THREE-DIMENSIONAL RIEMANNIAN MANIFOLDS OF C-CONULLITY TWO 219 11.1
INTRODUCTION 219 11.2 THE BASIC SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS
. . . .223 11.3 RIEMANNIAN INVARIANTS 227 11.4 ASYMPTOTIC FOLIATIONS AND
FOUR TYPES OF SPACES 229 11.5 THE EXPLICIT CLASSIFICATION OF
ASYMPTOTICALLY FOLIATED SPACES OF HYPERBOLIC TYPE 231 11.6 THE EXPLICIT
CLASSIFICATION OF ASYMPTOTICALLY FOLIATED SPACES OF ELLIPTIC TYPE 241
11.7 CONCLUDING REMARKS 249 12 MORE ABOUT CURVATURE HOMOGENEOUS SPACES
251 12.1 INTRODUCTION 251 12.2 EXAMPLES OF CURVATURE HOMOGENEOUS SPACES
OF NON-SYMMETRIC TYPE 253 12.2.1 ISOPARAMETRIC HYPERSURFACES IN SPHERES
253 12.2.2 CURVATURE HOMOGENEOUS HYPERSURFACES IN REAL SPACE FORMS 254
12.2.3 CURVATURE HOMOGENEOUS SPACES ON TWO-STEP SOLVABLE LIE GROUPS 255
12.3 THREE-DIMENSIONAL CURVATURE HOMOGENEOUS SPACES .... 259 12.3.1 THE
CASE P X = P 2 = PZ 260 12.3.2 THE CASE OF DISTINCT PI, P2, P3 264
12.3.3 MAIN EXISTENCE THEOREM 272 CONTENTS IX 12.4 CURVATURE HOMOGENEITY
IN HIGHER DIMENSIONS 273 12.5 EXTENSIONS 276 12.5.1 THE
PSEUDO-RIEMANNIAN CASE 276 12.5.2 THE AFFINE CASE 277 12.6 THE SINGER
THEOREM AND LOCAL HOMOGENEITY . 278 BIBLIOGRAPHY 283 INDEX 299
|
| any_adam_object | 1 |
| author | Boeckx, Eric Kowalski, Oldrich Vanhecke, Lieven 1939- |
| author_GND | (DE-588)114676887 |
| author_facet | Boeckx, Eric Kowalski, Oldrich Vanhecke, Lieven 1939- |
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| author_sort | Boeckx, Eric |
| author_variant | e b eb o k ok l v lv |
| building | Verbundindex |
| bvnumber | BV023777225 |
| classification_rvk | SK 350 |
| ctrlnum | (OCoLC)833083060 (DE-599)BVBBV023777225 |
| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 981022768X |
| language | English |
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| owner_facet | DE-634 DE-11 |
| physical | XVII, 300 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Boeckx, Eric Verfasser aut Riemannian manifolds of conullity two Eric Boeckx ; Oldrich Kowalski ; Lieven Vanhecke Singapore [u.a.] World Scientific 1996 XVII, 300 S. txt rdacontent n rdamedia nc rdacarrier Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Symmetrischer Raum (DE-588)4184206-6 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 s DE-604 Symmetrischer Raum (DE-588)4184206-6 s Kowalski, Oldrich Verfasser aut Vanhecke, Lieven 1939- Verfasser (DE-588)114676887 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017419437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boeckx, Eric Kowalski, Oldrich Vanhecke, Lieven 1939- Riemannian manifolds of conullity two Riemannscher Raum (DE-588)4128295-4 gnd Symmetrischer Raum (DE-588)4184206-6 gnd |
| subject_GND | (DE-588)4128295-4 (DE-588)4184206-6 |
| title | Riemannian manifolds of conullity two |
| title_auth | Riemannian manifolds of conullity two |
| title_exact_search | Riemannian manifolds of conullity two |
| title_full | Riemannian manifolds of conullity two Eric Boeckx ; Oldrich Kowalski ; Lieven Vanhecke |
| title_fullStr | Riemannian manifolds of conullity two Eric Boeckx ; Oldrich Kowalski ; Lieven Vanhecke |
| title_full_unstemmed | Riemannian manifolds of conullity two Eric Boeckx ; Oldrich Kowalski ; Lieven Vanhecke |
| title_short | Riemannian manifolds of conullity two |
| title_sort | riemannian manifolds of conullity two |
| topic | Riemannscher Raum (DE-588)4128295-4 gnd Symmetrischer Raum (DE-588)4184206-6 gnd |
| topic_facet | Riemannscher Raum Symmetrischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017419437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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