Semi-invariant warped product submanifolds of almost contact manifolds
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
Journal of Inequalities and Applications 2012, 2012:127 doi:10.1186/1029-242X-2012-127Published: 7 June 2012
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.