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

<abstract><p>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.</p></abstract>

Para-Kenmotsu manifolds admitting semi-symmetric structures

The object of the present paper is to study para-Kenmotsu manifolds satisfying different conditions of semi-symmetric type.

Static Perfect Fluid Space-Time on Almost Kenmotsu Manifolds

In this work, we intend to investigate the characteristics of static perfect fluid space-time metrics on almost Kenmotsu manifolds. At first we prove that if a Kenmotsu manifold $M$ is the spatial factor of static perfect fluid space-time then it is $\eta$-Einstein. Moreover, if the Reeb vector field $\xi$ leaves the scalar curvature invariant, then $M$ is Einstein. Next we consider static perfect fluid space-time on almost Kenmotsu $(\kappa,\mu)'$-manifolds and give some characteristics under certain conditions.

Some type of semisymmetry on two classes of almost Kenmotsu manifolds

The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a (k, µ)-almost Kenmotsu manifold satisfying the curvature condition Q · R = 0 is locally isometric to the hyperbolic space ℍ2 n +1(−1). Also in (k, µ)-almost Kenmotsu manifolds the following conditions: (1) local symmetry (∇R = 0), (2) semisymmetry (R·R = 0), (3) Q(S, R) = 0, (4) R·R = Q(S, R), (5) locally isometric to the hyperbolic space ℍ2 n +1(−1) are equivalent. Further, it is proved that a (k, µ)′ -almost Kenmotsu manifold satisfying Q · R = 0 is locally isometric to ℍ n +1(−4) × ℝ n and a (k, µ)′ -almost Kenmotsu manifold satisfying any one of the curvature conditions Q(S, R) = 0 or R · R = Q(S, R) is either an Einstein manifold or locally isometric to ℍ n +1(−4) × ℝ n . Finally, an illustrative example is presented.

ETA-RICCI SOLITONS ON LORENTZIAN PARA-KENMOTSU MANIFOLDS

The objective of present research article is to investigate the geometric properties of $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. In this manner, we consider $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying $R\cdot S=0$. Further, we obtain results for $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds with quasi-conformally flat property. Moreover, we get results for $\eta$-Ricci solitons in Lorentzian para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, $\eta$-quasi-conformally semi-symmetric, $\eta$-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper $\eta$-Ricci solitons.

On Kenmotsu manifolds admitting η-Ricci-Yamabe solitons

The objective of this paper is to deal with Kenmotsu manifolds admitting [Formula: see text]-Ricci-Yamabe solitons. First, it is proved that if a Kenmotsu manifold [Formula: see text] which admits an [Formula: see text]-Ricci-Yamabe soliton, then the manifold [Formula: see text] is Einstein and is of constant scalar curvature. Then, some important characterizations, which classify Kenmotsu manifolds admitting such solitons, are obtained and an example given which supports our results.

Almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in f-kenmotsu manifolds

In this paper, we study almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in 3-dimensional [Formula: see text]-Kenmotsu manifolds.