Author

# 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.

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TL;DR: In this paper , the authors studied α-cosymplectic manifold and showed that the Ricci tensor tensor is a semisymmetric manifold, which is an extension of the RICCI tensor.

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.

4 citations

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TL;DR: The main purpose of as mentioned in this paper is to study and explore some characteristics of static perfect fluid space-time on paracontact metric manifolds, and a suitable example has been constructed to show the existence of static ideal fluid space time on a 3-manifold.

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.

1 citations

##### Cited by

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TL;DR: In this paper , the authors investigated the properties of a 3-dimensional Kenmotsu manifold satisfying certain curvature conditions endowed with Ricci solitons and showed that such a manifold is φ-Einstein.

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.

1 citations

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TL;DR: In this paper , the authors concentrate on hyper generalized and quasi-generalized φ-varphi-recurrent π-cosymplectic manifolds and obtain some significant characterizations which classify such 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.

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TL;DR: In this article , the Schouten-van Kampen connection on α-cosymplectic manifolds admits pseudo-projective and W8-curvature tensors.

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.

TL;DR: In this paper , the authors concentrate on hyper generalized φ -recurrent α -cosymplectic manifolds and quasi generalized ε-generalized φ-recurrent ε -recurrence α -co-symmetric manifold and obtain some significant characterizations which classify such 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.