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Mathematics 2019, 7(2), 112; https://doi.org/10.3390/math7020112

Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons

Department of Mathematics, College of Science, King Khalid University, 9004 Abha, Saudi Arabia
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Received: 2 January 2019 / Revised: 14 January 2019 / Accepted: 18 January 2019 / Published: 22 January 2019
(This article belongs to the Special Issue Differential Geometry of Special Mappings)
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Abstract

The purpose of this article is to obtain geometric conditions in terms of gradient Ricci curvature, both necessary and sufficient, for a warped product semi-slant in a Kenmotsu space form, to be either CR-warped product or simply a Riemannian product manifold when a basic inequality become equality. The next purpose of this paper to find the necessary condition admitting gradient Ricci soliton, that the warped product semi-slant submanifold of Kenmotsu space form, is an Einstein warped product. We also discuss some obstructions to these constructions in more detail. View Full-Text
Keywords: warped products; Kenmotsu space forms; Euler-Lagrange equation; Ricci curvature; gradient Ricci soliton; gradient Ricci soliton warped product warped products; Kenmotsu space forms; Euler-Lagrange equation; Ricci curvature; gradient Ricci soliton; gradient Ricci soliton warped product
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Alkhaldi, A.H.; Ali, A. Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons. Mathematics 2019, 7, 112.

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