HOMOGENEOUS STRUCTURES ON KAEHLER SUBMANIFOLDS OF COMPLEX PROJECTIVE SPACES

摘要

In this paper we give a differential characterization of homogeneous Kaehler submanifolds of complex projective spaces in terms of the existence of a tensor field, the homogeneous structure S. We show that for any m∈M, S_m determines a unitary representation whose orbit at m is a compact, complete Kaehler submanifold which extends M. We consider the U(n) x U(N - n) (n = dim_cM) module of the space of these tensors and we find its irreducible factors.