This publication offers the 1st unified exam of the connection among Radon transforms on symmetric areas of compact kind and the infinitesimal models of 2 primary tension difficulties in Riemannian geometry. Its fundamental concentration is the spectral pressure challenge: Can the metric of a given Riemannian symmetric area of compact sort be characterised through 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 an identical size isometric to the canonical metric?

The authors comprehensively deal with the consequences pertaining to Radon transforms and the infinitesimal types of those difficulties. Their major consequence means that such a lot Grassmannians are spectrally inflexible to the 1st order. this can be quite vital, for there are nonetheless few isospectrality effects for absolutely curved areas and those are the 1st such effects for symmetric areas of compact form of rank >1. The authors make the most the speculation of overdetermined partial differential equations and harmonic research on symmetric areas to supply standards for infinitesimal stress that practice to a wide category of spaces.

quite a lot of easy fabric approximately Riemannian geometry, symmetric areas, and Radon transforms is incorporated in a transparent and stylish presentation that may be beneficial to researchers and complicated scholars in differential geometry.