Mendeley出力
＜図書＞
Radon transforms and the rigidity of the Grassmannians
| 責任表示 | Jacques Gasqui and Hubert Goldschmidt |
|---|---|
| シリーズ | Annals of mathematics studies ; no. 156 |
| データ種別 | 図書 |
| 出版情報 | Princeton ; Oxford : Princeton University Press , 2004 |
| 本文言語 | 英語 |
| 大きさ | xvii, 366 p. ; 24 cm |
| 概要 | 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. 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. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6829109 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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理系図3F 数理独自 | GASQ/10/2 | 2004 |
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023212003008314 |
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書誌詳細
| 一般注記 | Bibliography: p. [357]-361 Includes index |
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| 著者標目 | *Gasqui, Jacques Goldschmidt, Hubert, 1942- |
| 書誌ID | 1001403048 |
| ISBN | 0691118981 |
| NCID | BA65365053 |
| 巻冊次 | : hbk ; ISBN:0691118981 : pbk ; ISBN:069111899X |
| 登録日 | 2009.11.02 |
| 更新日 | 2009.11.02 |