Contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure

Volume 12, Issue 7, pp 440--449 http://dx.doi.org/10.22436/jnsa.012.07.03

Publication Date: March 09, 2019 Submission Date: December 01, 2018 Revision Date: February 14, 2019 Accteptance Date: February 21, 2019

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Authors

Amira A. Ishan - Department of Mathematics, Taif University, Taif, Kingdom of Saudi Arabia. Meraj Ali Khan - Department of Mathematics, University of Tabuk, Kingdom of Saudi Arabia.

Abstract

This paper studies the contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly Sasakian structure. Some Characterization of the existence of these warped product submanifolds are also obtained. We illustrate that the warping function is a harmonic function under certain conditions. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, and the equality case is also discussed. The results obtained in this paper generalize the results that have appeared in [I. Hasegawa, I. Mihai, Geom. Dedicata, \({\bf 102}\) (2003), 143--150], [I. Mihai, Geom. Dedicata, \({\bf 109}\) (2004), 165--173}], and [M. Atceken, Hacet. J. Math. Stat., \({\bf 44}\) (2015), 23--32].

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Keywords

• Warped products
• CR-submanifolds
• nearly Sasakian manifolds

MSC

•  53C25
•  53C40
•  53C42
•  53D15

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