Tohoku Mathematical Journal
2005

December
SECOND SERIES VOL. 57, NO. 4

Tohoku Math. J.
57 (2005), 521-540

Title PARALLEL KÄHLER SUBMANIFOLDS OF QUATERNIONIC KÄHLER SYMMETRIC SPACES

Author Dmitri V. Alekseevsky, Antonio J. Di Scala and Stefano Marchiafava

(Received November 27, 2003, revised August 12, 2004)
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.

2000 Mathematics Subject Classification. Primary 53C26; Secondary 53C55, 53C40.

Key words and phrases. Quaternionic Kähler manifolds, Kähler submanifolds, totally complex submanifolds.

To the top of this page

Back to the Contents