Radon Transforms and the Rigidity of the Grassmannians

Jacques Gasqui, Hubert Goldschmidt - Collection Annals of Mathematic Studies

366 pages, parution le 30/03/2004

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Résumé

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.

L'auteur - Jacques Gasqui

Jacques Gasqui, professeur honoraire des universités, nous donne ici son deuxième ouvrage (Le général Regard de la Grande guerre à la Résistance) sur les grandes figures des troupes de montagne originaires de l'Isère.

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L'auteur - Hubert Goldschmidt

Hubert Goldschmidt is Visiting Professor of Mathematics at Columbia University and Professeur des Universités in France.

Sommaire

Symmetric spaces and Einstein Manifolds
Radon transforms on symmetric spaces
Symmetric spaces of rank one
The real Grassmannians
The complex quadric
The rigidity of the complex quadric
The rigidity of the real Grassmannians
The complex Grassmannians
The rigidity of the complex Grassmannians
Products of symmetric spaces

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	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Jacques Gasqui, Hubert Goldschmidt
Collection	Annals of Mathematic Studies
Parution	30/03/2004
Nb. de pages	366
Format	15,5 x 23,5
Couverture	Broché
Poids	535g
Intérieur	Noir et Blanc
EAN13	9780691118994
ISBN13	978-0-691-11899-4