Parallel Kähler submanifolds of quaternionic Kähler symmetric spaces

Abstract

The non totally geodesic parallel $2n$-dimensional Kähler 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 Kähler submanifolds in a quaternionic Kähler symmetric space of non zero scalar curvature, i.e., in a Wolf space or in its non compact dual. They are exhausted by parallel Kähler submanifolds of a totally geodesic submanifold which is either an Hermitian symmetric space or a quaternionic projective space.