By Jacques Gasqui,Hubert Goldschmidt

ISBN-10: 0691118981

ISBN-13: 9780691118987

ISBN-10: 069111899X

ISBN-13: 9780691118994

This ebook presents the 1st unified exam of the connection among Radon transforms on symmetric areas of compact variety and the infinitesimal types of 2 basic pressure difficulties in Riemannian geometry. Its fundamental concentration is the spectral stress challenge: Can the metric of a given Riemannian symmetric house of compact variety be characterised by way of the spectrum of its Laplacian? It additionally addresses a query rooted within the Blaschke challenge: Is a Riemannian metric on a projective house whose geodesics are all closed and of a similar size isometric to the canonical metric?

The authors comprehensively deal with the implications referring to Radon transforms and the infinitesimal models of those difficulties. Their major outcome signifies that such a lot Grassmannians are spectrally inflexible to the 1st order. this can be relatively very important, for there are nonetheless few isospectrality effects for definitely curved areas and those are the 1st such effects for symmetric areas of compact form of rank >1. The authors take advantage of the speculation of overdetermined partial differential equations and harmonic research on symmetric areas to supply standards for infinitesimal stress that observe to a wide classification of spaces.

an excessive amount of easy fabric approximately Riemannian geometry, symmetric areas, and Radon transforms is incorporated in a transparent and stylish presentation that would be worthy to researchers and complex scholars in differential geometry.