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Open Access Research

An inequality for contact CR-warped product submanifolds of nearly cosymplectic manifolds

Siraj Uddin1* and Khalid Ali Khan2

Author Affiliations

1 Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, 50603, Malaysia

2 School of Engineering & Logistics, Faculty of Technology, Charles Darwin University, Darwin, NT, 0909, Australia

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Journal of Inequalities and Applications 2012, 2012:304  doi:10.1186/1029-242X-2012-304

Published: 18 December 2012

Abstract

Recently, Chen (Monatshefte Math. 133:177-195, 2001) established general sharp inequalities for CR-warped products in a Kaehler manifold. Afterward, Mihai obtained (Geom. Dedic. 109:165-173, 2004) the same inequalities for contact CR-warped product submanifolds of Sasakian space forms and derived some applications. In this paper, we obtain an inequality for the length of the second fundamental form of the warped product submanifold of a nearly cosymplectic manifold in terms of the warping function. The equality case is also discussed.

MSC: 53C40, 53C42, 53B25.

Keywords:
warped product; contact CR-submanifold; contact CR-warped product; nearly cosymplectic manifold