A Generalization of Cartan’s Identities for Isoparametric Hypersurfaces and Its Applications

摘要

We generalize Cartan’s identities for hypersurfaces with constant principal curvatures to those for endomorphisms on a subbundle of a tangent bundle with constant characteristic polynomial. As applications, we obtain Cartan’s identities for pseudo-Riemannian or equiaffine isoparametric hypersurfaces.