Parallel Kahler submanifolds of quaternionic Kahler symmetric spaces

概要

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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.
東北大学の論文