Certain conditions for a Riemannian manifold to be isometric with a sphere:Dedicated to Professor Kentaro Yano on his fiftieth birthday

Structures on Manifolds

The present paper is to deliberate the class of $ \epsilon $-Kenmotsu manifolds which admits conformal $ \eta $-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal $ \eta $-Ricci soliton of $ \epsilon $-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal $ \eta $-Ricci solitons on $ \epsilon $-Kenmotsu manifolds. Next, we consider gradient conformal $ \eta $-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for the existence of conformal $ \eta $-Ricci soliton on $ \epsilon $-Kenmotsu manifold.

Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds

On conharmonic transformations of weyl spaces

A Riemannian manifold (M,g) is called a quasi Einstein manifold if for any coordinate system in M, its Ricci tensor S satisfes S_(ij) = ag_(ij) + bA_iA_j for some scalars a and b, where A(X)=g(X, p) for some unit vector p. This class of manifolds is a generalization of Einstein manifolds which are quasi Einstein manifolds whose b=0. In this paper, we will give examples of these manifolds and we will show that on each coordinate system, a and b are unique.

On Quasi-Einstein Manifolds Which Are Not Einstein

Conformal Ricci soliton and quasi-Yamabe soliton on generalized Sasakian space form

In this paper we study ∗-η-Ricci soliton on Sasakian manifolds. Here, we have discussed some curvature properties on Sasakian manifold admitting ∗-η-Ricci soliton. We have obtained some significant...

∗-η-Ricci Soliton within the Framework of Sasakian Manifold

Abstract We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

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Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

The object of the present paper is to study some properties of (LCS)$_n$-manifolds whose metric is Yamabe soliton. We establish some characterization of (LCS)$_n$-manifolds when the soliton becomes steady. Next we have studied some certain curvature conditions of (LCS)$_n$-manifolds admitting Yamabe solitons. Lastly we construct a 3-dimensional (LCS)$_n$-manifold satisfying the results.

Santu Dey

Papers

Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds

Conformal Ricci soliton and quasi-Yamabe soliton on generalized Sasakian space form

∗-η-Ricci Soliton within the Framework of Sasakian Manifold

Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

Yamabe Solitons on (LCS)$_n$-manifolds