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International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 551-555
doi:10.1155/S0161171287000668

Totally umbilical CR-submanifolds of Semi-Riemannian Kaehler manifolds

K. L. Duggal and R. Sharma

Department of Mathematics and Statistics, University of Windsor, Windsor N9B 3P4, Ontario, Canada

Received 18 August 1986; Revised 20 October 1986

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study totally umbilical CR-submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.