Open Access Research

Semi-invariant warped product submanifolds of almost contact manifolds

Falleh R Al-Solamy1 and Meraj A Khan2*

Author Affiliations

1 Department of Mathematics, King Abdulaziz University, P.O. Box 80015, Jeddah 21589, Kingdom of Saudi Arabia

2 Department of Mathematics, University of Tabuk, Tabuk, Kingdom of Saudi Arabia

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Journal of Inequalities and Applications 2012, 2012:127 doi:10.1186/1029-242X-2012-127

Published: 7 June 2012

Abstract

In this article, we have obtained necessary and sufficient conditions in terms of canonical structure F on a semi-invariant submanifold of an almost contact manifold under which the submanifold reduced to semi-invariant warped product submanifold. Moreover, we have proved an inequality for squared norm of second fundamental form and finally, an estimate for the second fundamental form of a semi-invariant warped product submanifold in a generalized Sasakian space form is obtained, which extend the results of Chen, Al-Luhaibi et al., and Hesigawa and Mihai in a more general setting.

2000 Mathematics Subject Classification: 53C25; 53C40; 53C42; 53D15.

Keywords:
warped product; semi-invariant; almost contact metric manifold; generalized Sasakian space-form