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The present paper deals with the investigation of Para‐Kenmotsu manifolds admitting η$$ \eta $$‐Einstein solitons. Some necessary conditions for such manifolds to be Einstein are given, and it is proven that if a para‐Kenmotsu manifold E$$ E $$ admits an η$$ \eta $$‐Einstein soliton, then the manifold E$$ E $$ is Einstein. Then, some noteworthy characterizations that classify para‐Kenmotsu manifolds admitting such solitons are obtained. [ABSTRACT FROM AUTHOR]

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with - η -Ricci solitons. First we find some necessary conditions for such a manifold to be φ -Einstein. Then, we study the notion of - η -Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. [ABSTRACT FROM AUTHOR]

In this paper, we mainly focus on some classes of Ricci solitons on a Lorentzian α-Sasakian manifoldM and obtain some important results which classify such manifolds. We provide the necessary condition for which such a manifold M is Einstein-like. Also, we find that an η-Ricci soliton on M is steady if and only if M satisfies the curvature condition φ.P = 0. Finally, we give an example which verifies our results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with some geometric properties of an α-cosymplectic manifold. First, we give some classifications for an α-cosymplectic manifold endowed with some special vector fields such as projective, concircular and torse-forming. Then, we study αcosymplectic manifold admitting ƞ-Ricci solitons with projective, affine conformal vector fields. Finally, we obtain some characterizations for such a manifold to be Einstein, ƞ-Einstein, cosymplectic. [ABSTRACT FROM AUTHOR]

In the present paper, we will deal with a Kenmotsu manifold M. Firstly, we will study the notion of torse-forming vector field on such a manifold. Then, we will investigate some curvature conditions such as Q.M = 0 and C.Q = 0 on such a manifold and obtain some necessary conditions for such a manifold given as to be Einstein. Also, we will study a Kenmotsu manifold M admitting a Ricci soliton and give an example for this manifold. [ABSTRACT FROM AUTHOR]