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Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications

Akram Ali

http://orcid.org/0000-0002-6053-3031

Institute of Mathematical Science, Faculty of Sciences, University of Malaya 50603, Kuala Lumpur, Malaysia

E-mail Address: akramali133@gmail.com

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and

Cenap Ozel

Department of Mathematics, Dokuz Eylul University, Tinaztepe Campus Buca, Izmir 35160, Turkey

Department of Mathematics, Faculty Sciences, King Abdul Aziz University, Jeddah 21589, Saudi Arabia

E-mail Address: cenap.ozel@gmail.com

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https://doi.org/10.1142/S0219887817500426Cited by:23 (Source: Crossref)

Abstract

It is known from [K. Yano and M. Kon, Structures on Manifolds (World Scientific, 1984)] that the integration of the Laplacian of a smooth function defined on a compact orientable Riemannian manifold without boundary vanishes with respect to the volume element. In this paper, we find out the some potential applications of this notion, and study the concept of warped product pointwise semi-slant submanifolds in cosymplectic manifolds as a generalization of contact CR-warped product submanifolds. Then, we prove the existence of warped product pointwise semi-slant submanifolds by their characterizations, and give an example supporting to this idea. Further, we obtain an interesting inequality in terms of the second fundamental form and the scalar curvature using Gauss equation and then, derive some applications of it with considering the equality case. We provide many trivial results for the warped product pointwise semi-slant submanifolds in cosymplectic space forms in various mathematical and physical terms such as Hessian, Hamiltonian and kinetic energy, and generalize the triviality results for contact CR-warped products as well.

Keywords:

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