M. R. Amruthalakshmi

Bio: M. R. Amruthalakshmi is an academic researcher. The author has contributed to research in topics: Scalar curvature & Manifold (fluid mechanics). The author has an hindex of 1, co-authored 2 publications receiving 5 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.

Static perfect fluid space-time and paracontact metric geometry

Abstract: The main purpose of this paper is to study and explore some characteristics of static perfect fluid space-time on paracontact metric manifolds. First, we show that if a [Formula: see text]-paracontact manifold [Formula: see text] is the spatial factor of a static perfect fluid space-time, then [Formula: see text] is of constant scalar curvature [Formula: see text] and squared norm of the Ricci operator is given by [Formula: see text]. Next, we prove that if a [Formula: see text]-paracontact metric manifold [Formula: see text] with [Formula: see text] is a spatial factor of static perfect space-time, then for [Formula: see text], [Formula: see text] is flat, and for [Formula: see text], [Formula: see text] is locally isometric to the product of a flat [Formula: see text]-dimensional manifold and an [Formula: see text]-dimensional manifold of constant negative curvature [Formula: see text]. Further, we prove that if a paracontact metric 3-manifold [Formula: see text] with [Formula: see text] is a spatial factor of static perfect space-time, then [Formula: see text] is an Einstein manifold. Finally, a suitable example has been constructed to show the existence of static perfect fluid space-time on paracontact metric 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.