Parallel submanifolds in a quaternion projective space (Q1063883)

The purpose of the paper is to classify submanifolds with parallel second fundamental form in a quaternion projective space and its non-compact dual space. In order to do so, the author performs a systematic study of three kinds of immersions of a Riemannian manifold into a quaternion Kaehler manifold: totally real, totally complex and invariant immersions. He studies in detail totally complex immersions and produces models of totally complex parallel immersions of Hermitian symmetric spaces in a quaternion projective space.