Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 230374, 12 pages
http://dx.doi.org/10.1155/2011/230374
Research Article

Warped Product Semi-Invariant Submanifolds of Nearly Cosymplectic Manifolds

Siraj Uddin,1 S. H. Kon,1 M. A. Khan,2 and Khushwant Singh3

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

Received 20 April 2011; Accepted 16 June 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

We study warped product semi-invariant submanifolds of nearly cosymplectic manifolds. We prove that the warped product of the type 𝑀 ⟂ × 𝑓 𝑀 𝑇 is a usual Riemannian product of 𝑀 ⟂ and 𝑀 𝑇 , where 𝑀 ⟂ and 𝑀 𝑇 are anti-invariant and invariant submanifolds of a nearly cosymplectic manifold 𝑀 , respectively. Thus we consider the warped product of the type 𝑀 𝑇 × 𝑓 𝑀 ⟂ and obtain a characterization for such type of warped product.