Vector bundles, isoparametric functions and Radon transforms on symmetric spaces

Abstract

We systematically construct isoparametric functions on compact symmetric spaces using vector bundles and sections of the bundles. We establish a relation between invariants of vector bundles and invariants of hypersurfaces which are the level sets of the isoparametric functions induced by sections of the bundles. We hope that this approach provides a new method for computing invariants of hypersurfaces. The Radon transform is performed to derive isoparametric functions on spheres from our functions.