ON DIFFERENTIAL INVARIANTS OF HYPERPLANE SYSTEMS ON NONDEGENERATE EQUIVARIANT EMBEDDINGS OF HOMOGENEOUS SPACES

Abstract

Given a complex submanifold M of the projective space P(T), the hyperplane system R on M characterizes the projective embedding of M into P(T) in the following sense: for any two nondegenerate com- plex submanifolds MP(T) and M ' � P(T ' ), there is a projective linear transformation that sends an open subset of M onto an open subset of M ' if and only if (M,R) is locally equivalent to (M ' ,R ' ). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of lin- ear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane sys- tems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.