Parallel Kaehler submanifolds of quaternionic Kaehler 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.