Abstract and Applied Analysis
Volume 2012 (2012), Article ID 716967, 8 pages
http://dx.doi.org/10.1155/2012/716967
Research Article

A Classification of a Totally Umbilical Slant Submanifold of Cosymplectic Manifolds

Siraj Uddin,1 Cenap Ozel,2 and Viqar Azam Khan3

1Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
2Department of Mathematics, Abant Izzet Baysal University, 14268 Bolu, Turkey
3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Received 27 September 2011; Revised 26 December 2011; Accepted 26 December 2011

Academic Editor: Natig Atakishiyev

Copyright © 2012 Siraj Uddin et al. 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 slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold 𝑀 of a cosymplectic manifold 𝑀 is either an anti-invariant submanifold or a 1−dimensional submanifold. We show that every totally umbilical proper slant submanifold of a cosymplectic manifold is totally geodesic.