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HOME > Table of Contents and Abstracts > Vol. 57, No. 4
Tohoku Mathematical Journal
2005
December
SECOND SERIES VOL. 57, NO. 4
Tohoku Math. J.
57 (2005), 521-540
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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.
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