International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 405-408

On totally umbilical CR-submanifolds of a Kaehler manifold

M. A. Bashir

Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 4 June 1991; Revised 21 April 1992

Copyright © 1993 M. A. Bashir. 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.


Let M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector of M does not vanish, then M is either diffeomorphic to S3 or RP3 or a lens space Lp,q3.