On Ricci solitons in N(k)- quasi Einstein manifolds

Abstract

he object of the present paper is to study N(k)-quasi Einstein manifolds satisfying certain curvature conditions. Further we study gradient Ricci solitons on N(k)-quasi Einstein manifolds.

Kenmotsu manifolds admitting Schouten-Van Kampen Connection

“…In 2016, the authors in [21] explained the nature of Ricci solitons in f -Kenmotsu manifolds with a semi-symmetric non-metric connection. Ramesh Sharma et al [18] [19], De et al [4] [1], and Nagaraja et al [12] [11] [13] extensively studied Ricci solitons in contact metric manifolds in many different ways. This paper is structured as follows.…”

On generic submanifold of Sasakian manifold with concurrent vector field

“…Later, Perktaş and Keleş proved that if a 3 dimensional normal almost paracontact metric manifold admits a Ricci soliton, then it is shrinking (for details, see [21]). Ricci solitons have been studied in some di¤erent classes of contact geometry ( [3], [4], [15], [16], [18], [20]). Let (M ; g) be a Riemannian manifold andS be the Ricci tensor ofM .…”

Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection

“…By the way on a Riemannian manifold ( 2 +1 , ), a Ricci soliton is a soliton defined by Hamilton [4] similar to the Ricci flow and moves only with a one-parameter of the difeomorphism family. Also it is defined by the following relation (ℒ )( , ) + 2 ( , ) + 2 ( , ) = 0, (1) such that S is the Ricci tensor associated to , is the Lie derivative operator along the vector field and is a real scalar [5].…”