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Mathematical Problems in Engineering
Volume 2011, Article ID 516238, 9 pages
http://dx.doi.org/10.1155/2011/516238
Research Article

Totally Umbilical Proper Slant and Hemislant Submanifolds of an LP-Cosymplectic Manifold

1Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia
2Department of Mathematics, University of Tabouk, Tabouk, Saudi Arabia
3School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India

Received 13 December 2010; Accepted 15 April 2011

Academic Editor: Alex Elias-Zuniga

Copyright © 2011 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

In the present note, we study slant and hemislant submanifolds of an LP-cosymplectic manifold which are totally umbilical. We prove that every totally umbilical proper slant submanifold 𝑀 of an LP-cosymplectic manifold 𝑀 is either totally geodesic or if 𝑀 is not totally geodesic in 𝑀 then we derive a formula for slant angle of 𝑀. Also, we obtain the integrability conditions of the distributions of a hemi-slant submanifold, and then we give a result on its classification.