Radon transforms and the rigidity of the Grassmannians:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2004
|
| Series: | Annals of mathematics studies
156 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 366 S. |
| ISBN: | 069111899X 0691118981 |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Introduction ix
CHAPTER I
Symmetric spaces and Einstein manifolds
1. Riemannian manifolds 1
2. Einstein manifolds 15
3. Symmetric spaces 19
4. Complex manifolds 27
CHAPTER II
Radon transforms on symmetric spaces
1. Outline 32
2. Homogeneous vector bundles and harmonic analysis 32
3. The Guillemin and zero energy conditions 36
4. Radon transforms 41
5. Radon transforms and harmonic analysis 50
6. Lie algebras 58
7. Irreducible symmetric spaces 59
8. Criteria for the rigidity of an irreducible symmetric space 68
CHAPTER III
Symmetric spaces of rank one
1. Flat tori 75
2. The projective spaces 83
3. The real projective space 89
4. The complex projective space 94
5. The rigidity of the complex projective space 104
6. The other projective spaces 112
CHAPTER IV
The real Grassmannians
1. The real Grassmannians 114
2. The Guillemin condition on the real Grassmannians 126
vi TABLE OF CONTENTS
CHAPTER V
The complex quadric
1. Outline 134
2. The complex quadric viewed as a symmetric space 134
3. The complex quadric viewed as a complex hypersurface 138
4. Local Kahler geometry of the complex quadric 146
5. The complex quadric and the real Grassmannians 152
6. Totally geodesic surfaces and the infinitesimal orbit
of the curvature 159
7. Multiplicities 170
8. Vanishing results for symmetric forms 185
9. The complex quadric of dimension two 190
CHAPTER VI
The rigidity of the complex quadric
1. Outline 193
2. Total geodesic flat tori of the complex quadric 194
3. Symmetric forms on the complex quadric 199
4. Computing integrals of symmetric forms 204
5. Computing integrals of odd symmetric forms 209
6. Bounds for the dimensions of spaces of symmetric forms 218
7. The complex quadric of dimension three 223
8. The rigidity of the complex quadric 229
9. Other proofs of the infinitesimal rigidity of the quadric 232
10. The complex quadric of dimension four 234
11. Forms of degree one 237
CHAPTER VII
The rigidity of the real Grassmannians
1. The rigidity of the real Grassmannians 244
2. The real Grassmannians G^n 249
CHAPTER VIII
The complex Grassmannians
1. Outline 257
2. The complex Grassmannians 258
3. Highest weights of irreducible modules associated
with the complex Grassmannians 270
4. Functions and forms on the complex Grassmannians 274
TABLE OF CONTENTS vii
5. The complex Grassmannians of rank two 282
6. The Guillemin condition on the complex Grassmannians 287
7. Integrals of forms on the complex Grassmannians 293
8. Relations among forms on the complex Grassmannians 300
9. The complex Grassmannians G^n 303
CHAPTER IX
The rigidity of the complex Grassmannians
1. The rigidity of the complex Grassmannians 308
2. On the rigidity of the complex Grassmannians G^n 313
3. The rigidity of the quaternionic Grassmannians 323
CHAPTER X
Products of symmetric spaces
1. Guillemin rigidity and products of symmetric spaces 329
2. Conformally flat symmetric spaces 334
3. Infinitesimal rigidity of products of symmetric spaces 338
4. The infinitesimal rigidity of Gf2 340
References 357
Index 363
|
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| author | Gasqui, Jacques Goldschmidt, Hubert 1942- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV017979519 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:23:49Z |
| institution | BVB |
| isbn | 069111899X 0691118981 |
| language | English |
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| physical | XVII, 366 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Gasqui, Jacques Verfasser (DE-588)136201636 aut Radon transforms and the rigidity of the Grassmannians Jacques Gasqui and Hubert Goldschmidt Princeton [u.a.] Princeton Univ. Press 2004 XVII, 366 S. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 156 Graßmann-Mannigfaltigkeit - Radon-Transformation Radon-Transformation (DE-588)4479199-9 gnd rswk-swf Graßmann-Mannigfaltigkeit (DE-588)4158085-0 gnd rswk-swf Radon-Transformation (DE-588)4479199-9 s Graßmann-Mannigfaltigkeit (DE-588)4158085-0 s DE-604 Goldschmidt, Hubert 1942- Verfasser (DE-588)136201695 aut Annals of mathematics studies 156 (DE-604)BV000000991 156 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010772920&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gasqui, Jacques Goldschmidt, Hubert 1942- Radon transforms and the rigidity of the Grassmannians Annals of mathematics studies Graßmann-Mannigfaltigkeit - Radon-Transformation Radon-Transformation (DE-588)4479199-9 gnd Graßmann-Mannigfaltigkeit (DE-588)4158085-0 gnd |
| subject_GND | (DE-588)4479199-9 (DE-588)4158085-0 |
| title | Radon transforms and the rigidity of the Grassmannians |
| title_auth | Radon transforms and the rigidity of the Grassmannians |
| title_exact_search | Radon transforms and the rigidity of the Grassmannians |
| title_full | Radon transforms and the rigidity of the Grassmannians Jacques Gasqui and Hubert Goldschmidt |
| title_fullStr | Radon transforms and the rigidity of the Grassmannians Jacques Gasqui and Hubert Goldschmidt |
| title_full_unstemmed | Radon transforms and the rigidity of the Grassmannians Jacques Gasqui and Hubert Goldschmidt |
| title_short | Radon transforms and the rigidity of the Grassmannians |
| title_sort | radon transforms and the rigidity of the grassmannians |
| topic | Graßmann-Mannigfaltigkeit - Radon-Transformation Radon-Transformation (DE-588)4479199-9 gnd Graßmann-Mannigfaltigkeit (DE-588)4158085-0 gnd |
| topic_facet | Graßmann-Mannigfaltigkeit - Radon-Transformation Radon-Transformation Graßmann-Mannigfaltigkeit |
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