2019 # Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons

**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…

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“…This paper shows the relation between the notion of warped product manifold and homotopy-homology theory. Therefore, we hope that this paper will be of great interest with respect to the topology of Riemannian geometry [28][29][30][31][32][33][34][35] which may find possible applications in physics.…”

confidence: 99%

“…This paper shows the relation between the notion of warped product manifold and homotopy-homology theory. Therefore, we hope that this paper will be of great interest with respect to the topology of Riemannian geometry [28][29][30][31][32][33][34][35] which may find possible applications in physics.…”

confidence: 99%

“…When f is a constant map, a gradient Ricci-harmonic soliton turns into a gradient Ricci soliton [8]. For details about Ricci and gradient Ricci solitons see also [14][15][16][17][18][19] and [20].…”

confidence: 99%

“…More triviality results can be found in [3], that is, every compact gradient k-Yamabe soliton must have constant k-curvature and certain conditions over the gradient. On the other hand, Yamabe solitons and quasi-Yamabe solitons with concurrent vector fields are discussed in [6] and also in a great number of good results in [7][8][9][10][11][12][13][14][15][16][17][18]. Motivated by some previous results regarding the classification of the theory of solitons geometry; we shall study some geometric classifications notes for k-Yamabe solitons on Euclidean hypersurfaces, if it is a potential field, originated from their position vector fields.…”

confidence: 99%