Radon transforms and the rigidity of the Grassmannians:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2004]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 156 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Main description: This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary focus is the spectral rigidity problem: Can the metric of a given Riemannian symmetric space of compact type be characterized by means of the spectrum of its Laplacian? It also addresses a question rooted in the Blaschke problem: Is a Riemannian metric on a projective space whose geodesics are all closed and of the same length isometric to the canonical metric? The authors comprehensively treat the results concerning Radon transforms and the infinitesimal versions of these two problems. Their main result implies that most Grassmannians are spectrally rigid to the first order. This is particularly important, for there are still few isospectrality results for positively curved spaces and these are the first such results for symmetric spaces of compact type of rank 1. The authors exploit the theory of overdetermined partial differential equations and harmonic analysis on symmetric spaces to provide criteria for infinitesimal rigidity that apply to a large class of spaces. A substantial amount of basic material about Riemannian geometry, symmetric spaces, and Radon transforms is included in a clear and elegant presentation that will be useful to researchers and advanced students in differential geometry |
| Beschreibung: | 1 Online-Ressource (384 S.) |
| ISBN: | 9781400826179 |
| DOI: | 10.1515/9781400826179 |
Internformat
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| 490 | 1 | |a Annals of Mathematics Studies |v number 156 | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Gasqui, Jacques Goldschmidt, Hubert 1942- |
| author_GND | (DE-588)136201636 (DE-588)136201695 |
| author_facet | Gasqui, Jacques Goldschmidt, Hubert 1942- |
| author_role | aut aut |
| author_sort | Gasqui, Jacques |
| author_variant | j g jg h g hg |
| building | Verbundindex |
| bvnumber | BV042522264 |
| classification_rvk | SI 830 SK 370 SK 450 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)890450524 (DE-599)BVBBV042522264 |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400826179 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:01Z |
| institution | BVB |
| isbn | 9781400826179 |
| language | English |
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| spelling | Gasqui, Jacques (DE-588)136201636 aut Radon transforms and the rigidity of the Grassmannians Princeton, N.J. Princeton University Press [2004] © 2004 1 Online-Ressource (384 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 156 Main description: This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary focus is the spectral rigidity problem: Can the metric of a given Riemannian symmetric space of compact type be characterized by means of the spectrum of its Laplacian? It also addresses a question rooted in the Blaschke problem: Is a Riemannian metric on a projective space whose geodesics are all closed and of the same length isometric to the canonical metric? The authors comprehensively treat the results concerning Radon transforms and the infinitesimal versions of these two problems. Their main result implies that most Grassmannians are spectrally rigid to the first order. This is particularly important, for there are still few isospectrality results for positively curved spaces and these are the first such results for symmetric spaces of compact type of rank 1. The authors exploit the theory of overdetermined partial differential equations and harmonic analysis on symmetric spaces to provide criteria for infinitesimal rigidity that apply to a large class of spaces. A substantial amount of basic material about Riemannian geometry, symmetric spaces, and Radon transforms is included in a clear and elegant presentation that will be useful to researchers and advanced students in differential geometry 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 1\p DE-604 Goldschmidt, Hubert 1942- (DE-588)136201695 aut Erscheint auch als Druck-Ausgabe 0-691-11898-1 Annals of Mathematics Studies number 156 (DE-604)BV040389493 156 https://doi.org/10.1515/9781400826179?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826179&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gasqui, Jacques Goldschmidt, Hubert 1942- Radon transforms and the rigidity of the Grassmannians Annals of Mathematics Studies 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 |
| title_fullStr | Radon transforms and the rigidity of the Grassmannians |
| title_full_unstemmed | Radon transforms and the rigidity of the Grassmannians |
| title_short | Radon transforms and the rigidity of the Grassmannians |
| title_sort | radon transforms and the rigidity of the grassmannians |
| topic | Radon-Transformation (DE-588)4479199-9 gnd Graßmann-Mannigfaltigkeit (DE-588)4158085-0 gnd |
| topic_facet | Radon-Transformation Graßmann-Mannigfaltigkeit |
| url | https://doi.org/10.1515/9781400826179?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826179&searchTitles=true |
| volume_link | (DE-604)BV040389493 |
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