Radon Transforms and the Rigidity of the Grassmannians 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Gasqui, Jacques; Goldschmidt, Hubert; 作者

译者

2004-1 出版日期

376 页数

$ 107.35 价格

丛书系列

9780691118994 图书编码

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Radon Transforms and the Rigidity of the Grassmannians 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Radon Transforms and the Rigidity of the Grassmannians 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

Radon Transforms and the Rigidity of the Grassmannians 在线电子书图书描述

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.

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