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Parallel Kahler submanifolds of quaternionic Kahler symmetric spaces

Summary: Parallel Kšahler submanifolds
of quaternionic Kšahler symmetric spaces
D. V. Alekseevsky, A. J. Di Scala and S. Marchiafava
November 6, 2003
The non totally geodesic parallel Kšahler submanifolds (M2n, J1) of the
quaternionic space HPn were classified by K. Tsukada, [Tsu2]. Here we
give the complete classification of non totally geodesic immersions of parallel
Kšahler submanifolds (M2m, J1) in a quaternionic Kšahler symmetric space
(M4n, g, Q) of non zero scalar curvature, i.e. in a Wolf space W or in its
non compact dual. They are exhausted by parallel Kšahler submanifolds of
a totally geodesic submanifold M which is either an Hermitian symmetric
space or a quaternionic projective space.
1 Introduction.
Let (M4n
, g, Q) be a quaternionic Kšahler manifold with metric g and parallel
quaternionic structure Q. A submanifold M2m
together with a section J1 (Q)|M
such that J2
1 = -1 and J1TM = TM is called Kšahler if J1 is parallel with respect


Source: Alekseevsky, Dmiti - Department of Mathematics, University of Hull


Collections: Computer Technologies and Information Sciences