I. Unal

Bio: I. Unal is an academic researcher. The author has contributed to research in topics: Einstein tensor & Tensor (intrinsic definition). The author has an hindex of 1, co-authored 2 publications receiving 4 citations.

∗ -Ricci Tensor on α -Cosymplectic Manifolds

Abstract: In this paper, we study α-cosymplectic manifold $M$ admitting $\ast$ -Ricci tensor. First, it is shown that a $\ast$ -Ricci semisymmetric manifold $M$ is $\ast$ -Ricci flat and a $\varphi$ -conformally flat manifold $M$ is an $\eta$ -Einstein manifold. Furthermore, the $\ast$ -Weyl curvature tensor ${\mathcal{W}}^{\ast }$ on $M$ has been considered. Particularly, we show that a manifold $M$ with vanishing $\ast$ -Weyl curvature tensor is a weak $\varphi$ -Einstein and a manifold $M$ fulfilling the condition $R\left(E_1,E_2\right)\cdot {\mathcal{W}}^{\ast }=0$ is $\eta$ -Einstein manifold. Finally, we give a characterization for α-cosymplectic manifold $M$ admitting $\ast$ -Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting $\ast$ -Ricci soliton and almost $\ast$ -Ricci soliton are drawn.

Geometry of Kenmotsu manifolds admitting Z-tensor

Abstract: The object of this paper is to study Kenmotsu manifolds admitting Z−tensor, which is a generalization of Einstein tensor that comes from general relativity. We define a special type of quarter-symmetric non-metric ϕ and η-connection on a Kenmotsu manifold and we examine some geometric properties of such manifolds with Z−tensor. Some semi-symmetry conditions related to Z−tensor are studied on Kenmotsu manifolds and finally, we observe our results on a 5-dimensional Kenmotsu manifold.

Certain Curvature Conditions on Kenmotsu Manifolds and ★-η;-Ricci Solitons

Abstract: 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.

On Some Classes of Generalized Recurrent $\alpha-$Cosymplectic Manifolds

Abstract: In this paper, we concentrate on hyper generalized $\varphi-$recurrent $\alpha-$cosymplectic manifolds and quasi generalized $\varphi-$recurrent $\alpha-$cosymplectic manifolds and obtain some significant characterizations which classify such manifolds.

A note on α-cosymplectic manifolds with respect to the Schouten-van Kampen connection

Abstract: This paper is concerned with some results on α-cosymplectic manifolds admitting the Schouten-van Kampen connection with pseudo-projective and W8-curvature tensor.

On Some Classes of Generalized Recurrent α -Cosymplectic Manifolds

Abstract: A bstract . In this paper, we concentrate on hyper generalized φ -recurrent α -cosymplectic manifolds and quasi generalized φ -recurrent α -cosymplectic manifolds and obtain some significant characterizations which classify such manifolds.