PROJECTIVELY FLAT IMMERSIONS OF HERMITIAN SYMMETRIC SPACES OF COMPACT TYPE

Abstract

In this article, we define a projectively flat map of a compact Kähler manifold into the complex Grassmannian manifold, which is a kind of extension of a holomorphic map into the complex projective space. Then we show a rigidity theorem of a holomorphic isometric projectively flat immersion of Hermitian symmetric spaces of compact type. As an application, we classify holomorphic isometric projectively flat immersions of compact Kähler manifolds with parallel second fundamental form.