International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 405-408
doi:10.1155/S016117129300050X
On totally umbilical CR-submanifolds of a Kaehler manifold
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.
Abstract
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.