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

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.