Some special vector fields on a cosymplectic manifold admitting a Ricci soliton

Abstract

In this paper, we deal with the geometric properties of cosymplectic manifold. We give some classifications for a cosymplectic manifold endowed with some special vector fields, such as contact, concircular, recurrent, torse-forming and some characterizations for such a manifold admitting a Ricci soliton given as to be Einstein, η−Einstein, almost quasi-Einstein and nearly quasi-Einstein.

Geometry of $\ast$-$k$-Ricci-Yamabe soliton and gradient $\ast$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

“…Recently, Wang [50] proved that if the metric of a Kenmotsu 3-manifold represents a * -Ricci soliton, then the manifold is locally isometric to the hyperbolic space H 3 (−1). Moreover, we can get more latest studies equipped with soliton geometry in [12,18,31,39,40,55].…”

Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$

“…The concept of Ricci solitons has become a fascinating issue in the differential geometry and this concept has been studied on various submanifolds of Riemannian manifolds. For some applications on Ricci solitons, we touch on [1][2][3][4][5][6][7][8], etc. A (semi-) Riemannian manifold (M, g) is said to be a Ricci soliton if…”

Quarter-Symmetric Metric Connection on a Cosymplectic Manifold

“…Moreover, there is an example of a compact cosymplectic manifold that is not a global product of a compact Kähler manifold with a circle [4]. In [5], the author studied contact, concircular, recurrent, and torse-forming vector fields on cosymplectic manifolds. Note that a different definition of cosymplectic manifolds was used in some papers (for instance, see [2,6,7]).…”

“…on the almost-contact metric manifold, = 0 holds. Taking into account Equation(5), it follows that on the almost-contact metric manifold, the torsion tensor is parallel to the connection 1 = 0. In the paper[11], quarter-symmetric metric connections (4) are studied on almost-contact metric manifolds, and the properties of the torsion tensor 1…”