Another class of warped product CR-submanifolds in Kenmotsu manifolds

Volume 17, Issue 1, pp 148-157 http://dx.doi.org/10.22436/jmcs.017.01.13

Publication Date: March 15, 2017 Submission Date: December 12, 2016

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Authors

Siraj Uddin - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Azeb Alghanemi - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Monia Fouad Naghi - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Falleh Rijaullah Al-Solamy - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.

Abstract

Recently, Arslan et al. [K. Arslan, R. Ezentas, I. Mihai, C. Murathan, J. Korean Math. Soc., 42 (2005), 1101–1110] studied contact CR-warped product submanifolds of the form \(M_\top \times_f M_\bot\) of a Kenmotsu manifold \(\widetilde{M}\), where \(M_\top\) and \(M_\bot\) are invariant and anti-invariant submanifolds of \(\widetilde{M}\), respectively. In this paper, we study the warped product submanifolds by reversing these two factors, i.e., the warped products of the form \(M_\bot \times_f M_\top\) which have not been considered in earlier studies. On the existence of such warped products, a characterization is given. A sharp estimation for the squared norm of the second fundamental form is obtained, and in the statement of inequality, the equality case is considered. Finally, we provide two examples of non-trivial warped product submanifolds.

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Keywords

• Warped products
• contact CR-submanifolds
• mixed totally geodesic
• contact CR-warped products
• Kenmotsu manifolds.

MSC

•  53C25
•  53C40
•  53C42
•  53B25

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