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 some obstructions to these constructions in more detail.

Geometric Inequalities of Warped Product Submanifolds and Their Applications

“…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.…”

On sequential warped product manifolds admitting gradient Ricci-harmonic solitons

“…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].…”

Geometry of k-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields

“…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.…”