# Application of Hopf's lemma on contact CR-warped product submanifolds of a nearly Kenmotsu manifold

Document Type: Research Paper

Authors

1 ‎Department of Mathematics, ‎University of Tabuk‎, ‎Kingdom of Saudi Arabia.

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

Abstract

In this paper we consider contact CR-warped product submanifolds of the type $M = N_T\times_f N_\perp$, of a nearly Kenmotsu generalized Sasakian space form $\bar M(f_1‎, ‎f_2‎, ‎f_3)$ and by use of Hopf's Lemma we show that $M$ is simply contact CR-product under certain condition‎. ‎Finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case is discussed‎. ‎The results in this paper generalize existing results in the literature.

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### History

• Receive Date: 22 March 2015
• Revise Date: 16 October 2015
• Accept Date: 16 October 2015