Certain conditions for a Riemannian manifold to be isometric with a sphere:Dedicated to Professor Kentaro Yano on his fiftieth birthday

Integral formulas in Riemannian geometry

In this paper, we study para-Sasakian manifold (M,g) whose metric g is an η-Ricci soliton (g,V ) and almost η-Ricci soliton. We prove that, if g is an η-Ricci soliton, then either M is Einstein and...

η-Ricci solitons and almost η-Ricci solitons on para-Sasakian manifolds

Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

https://www.degruyter.com/document/doi/10.1515/math-2019-0056/pdf

*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

Abstract We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

/pdf/geometry-of-conformal-e-ricci-solitons-and-conformal-e-ricci-2pjjz7h3.pdf

Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

In this paper we initiate the study of quasi Yamabe soliton on 3-dimensional
contact metric manifold with Q\varphi=\varphi Q and prove that if a
3-dimensional contact metric manifold M such that Q\varphi=\varphi Q admits a
quasi Yamabe soliton with non-zero soliton vector field V being point-wise
collinear with the Reeb vector field {\xi}, then V is a constant multiple of
{\xi}, the scalar curvature is constant and the manifold is Sasakian. Moreover,
V is Killing. Finally, we prove that if M is a 3-dimensional compact contact
metric manifold such that Q\varphi=\varphi Q endowed with a quasi Yamabe
soliton, then either M is flat or soliton is trivial.

/pdf/quasi-yamabe-solitons-on-3-dimensional-contact-metric-3iqrnn9x.pdf

Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Q\varphi=\varphi Q

On E-Bochner Curvature Tensor of Contact Metric Generalized $(\kappa,\mu)$ Space Forms

In this paper we study Kenmotsu manifold admitting a semi-symmetric metric connection whose concircular curvature tensor satisfies certain curvature conditions.

/pdf/curvature-properties-of-kenmotsu-manifold-admitting-semi-dwb5e3xsrc.pdf

Curvature properties of Kenmotsu manifold admitting semi-symmetric metric connection

Abstract In this paper, we aim to study a special type of metric called almost * {*} -η-Ricci soliton on the special class of contact pseudo-Riemannian manifold. First, we prove that a Kenmotsu pseudo-Riemannian metric as an * {*} -η-Ricci soliton is Einstein if either it is η-Einstein or the potential vector field V is an infinitesimal contact transformation. Further, we prove that if a Kenmotsu pseudo-Riemannian manifold admits an almost * {*} -η-Ricci soliton with a Reeb vector field leaving the scalar curvature invariant, then it is an Einstein manifold. Finally, we present an example of * {*} -η-Ricci solitons which illustrate our results.

Almost *-η-Ricci solitons on Kenmotsu pseudo-Riemannian manifolds

/pdf/wormhole-solutions-in-f-r-l-m-gravity-iabcqhme.pdf

V. Venkatesha

Papers

Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Q\varphi=\varphi Q

On E-Bochner Curvature Tensor of Contact Metric Generalized $(\kappa,\mu)$ Space Forms

Curvature properties of Kenmotsu manifold admitting semi-symmetric metric connection

Almost *-η-Ricci solitons on Kenmotsu pseudo-Riemannian manifolds

Wormhole solutions in $f(R,L_m)$ gravity