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Radon transforms and the rigidity of the grassmannians

Author: Jacques Gasqui
Publisher: Princeton, N.J. ; Woodstock : Princeton University Press, 2004.
Series: Annals of mathematics studies, no. 156.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Gasqui, Jacques.
Radon transforms and the rigidity of the grassmannians.
Princeton, N.J. ; Woodstock : Princeton University Press, 2004
(OCoLC)56446722
Named Person: Hubert Goldschmidt; Hubert Goldschmidt
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jacques Gasqui
ISBN: 9781400826179 1400826179 9780691118987 0691118981
OCLC Number: 437268713
Language Note: In English.
Description: 1 online resource (333 pages).
Contents: Frontmatter --
TABLE OF CONTENTS --
INTRODUCTION --
Chapter I. Symmetric Spaces and Einstein Manifolds --
Chapter II. Radon Transforms on Symmetric Spaces --
Chapter III. Symmetric Spaces of Rank One --
Chapter IV. The Real Grassmannians --
Chapter V. The Complex Quadric --
Chapter VI. The Rigidity of the Complex Quadric --
Chapter VII. The Rigidity of the Real Grassmannians --
Chapter VIII. The Complex Grassmannians --
Chapter IX. The Rigidity of the Complex Grassmannians --
Chapter X. Products of Symmetric Spaces --
References --
Index.
Series Title: Annals of mathematics studies, no. 156.
Responsibility: Jacques Gasqui and Hubert Goldschmidt.

Abstract:

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? Th.

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