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

/pdf/ricci-solitons-and-certain-related-metrics-on-almost-co-246jt351lr.pdf

Ricci Solitons and Certain Related Metrics on Almost Co-Kaehler Manifolds

The aim of this paper, is to study the Riemann soliton and gradient almost Riemann soliton on certain class of almost Kenmotsu manifolds. Also, some suitable examples of Kenmotsu and (κ,μ)′-almost ...

Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds

In the present paper, we have studied M -projectively flat generalized Sasakian space form, η-Einstein generalized Sasakian space form and irrotational M -projective curvature tensor on a Sasakian space form.

/pdf/on-m-projective-curvature-tensor-of-a-generalized-sasakian-pmw3hhsz21.pdf

On M-projective curvature tensor of a generalized Sasakian space form

Constraining anisotropic cosmological model in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e684" altimg="si6.svg"><mml:mrow><mml:mi mathvariant="script" class="mathpzc">f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>,</mml:mo>

/pdf/certain-results-on-kenmotsu-pseudo-metric-manifolds-2a2k554oj7.pdf

V. Venkatesha

Papers

Ricci Solitons and Certain Related Metrics on Almost Co-Kaehler Manifolds

Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds

On M-projective curvature tensor of a generalized Sasakian space form

Constraining anisotropic cosmological model in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e684" altimg="si6.svg"><mml:mrow><mml:mi mathvariant="script" class="mathpzc">f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>,</mml:mo>

Certain results on Kenmotsu pseudo-metric manifolds