Parallel Kahler submanifolds of quaternionic Kahler symmetric spaces

摘要

The non totally geodesic parallel 2n-dimensional Kahler submanifolds of the n-dimensional quaternionic projective space were classified by K. Tsukada. Here we give the complete classification of non totally geodesic immersions of parallel 2m-dimensional Kahler submanifolds in a quaternionic Kahler symmetric space of non zero scalar curvature. i.e., in a Wolf space or in its non compact dual. They are exhausted by parallel Kahler submanifolds of a totally geodesic submanifold which is either an Hermitian symmetric space or a quaternionic projective space.