O'Reilly logo

Radon Transforms and the Rigidity of the Grassmannians (AM-156) by Hubert Goldschmidt, Jacques Gasqui

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

INTRODUCTION

This monograph is motivated by a fundamental rigidity problem in Riemannian geometry: determine whether the metric of a given Rieman-nian symmetric space of compact type can be characterized by means of the spectrum of its Laplacian. An infinitesimal isospectral deformation of the metric of such a symmetric space belongs to the kernel of a certain Radon transform defined in terms of integration over the flat totally geodesic tori of dimension equal to the rank of the space. Here we study an infinitesimal version of this spectral rigidity problem: determine all the symmetric spaces of compact type for which this Radon transform is injective in an appropriate sense. We shall both give examples of spaces which are not infinitesimally ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required