Theorems of Gauss-Bonnet and Chern-Lashof Types in a Simply Connected Symmetric Space of Non-Positive Curvature

Abstract

In this paper, we shall generalize the Gauss-Bonnet and Chern-Lashof theorems to compact submanifolds in a simply connected symmetric space of non-positive curvature. Those proofs are performed by applying the Morse theory to squared distance functions because height functions are not defined.