scholarly journals A Note on LP -Sasakian Manifolds with Almost Quasi-Yamabe Solitons

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Sunil Kumar Yadav ◽  
D. L. Suthar ◽  
Biniyam Shimelis
Keyword(s):  
Vector Field ◽  
Sasakian Manifolds ◽  
Potential Vector ◽  
Metric Connection ◽  
Yamabe Solitons ◽  
Potential Vector Field

We categorize almost quasi-Yamabe solitons on LP -Sasakian manifolds and their CR -submanifolds whose potential vector field is torse-forming, admitting a generalized symmetric metric connection of type α , β . Finally, a nontrivial example is provided to confirm some of our results.

scholarly journals Yamabe Solitons with potential vector field as torse forming

Cubo (Temuco) ◽  
2018 ◽  
Vol 20 (3) ◽  
pp. 37-47
Author(s):  
Yadab ChandraMandal ◽  
Shyamal Kumar Hui
Keyword(s):  
Vector Field ◽  
Potential Vector ◽  
Yamabe Solitons ◽  
Potential Vector Field

The k-almost Yamabe solitons and almost coKähler manifolds

2021 ◽  
pp. 2150179
Author(s):  
Xiaomin Chen ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Riemannian Product ◽  
Reeb Vector ◽  
Potential Vector ◽  
Reeb Vector Field ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Yamabe Solitons ◽  
Potential Vector Field

In this paper, we study almost coKähler manifolds admitting [Formula: see text]-almost Yamabe solitons [Formula: see text]. First, we obtain a classification of almost coKähler [Formula: see text]-manifolds admitting nontrivial closed [Formula: see text]-almost Yamabe solitons. Next, we consider an almost [Formula: see text]-coKähler manifold admitting a nontrivial [Formula: see text]-almost Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector field. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector field, we also obtain two results.

Almost quasi-Yamabe solitons on almost cosymplectic manifolds

2020 ◽  
Vol 17 (05) ◽  
pp. 2050070
Author(s):  
Xiaomin Chen
Keyword(s):  
Vector Field ◽  
Riemannian Product ◽  
Reeb Vector ◽  
Potential Vector ◽  
Cosymplectic Manifolds ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Yamabe Solitons ◽  
Yamabe Soliton ◽  
Potential Vector Field

In this paper, we study almost cosymplectic manifolds admitting almost quasi-Yamabe solitons [Formula: see text]. First, we prove that an almost cosymplectic [Formula: see text]-manifold is locally isomorphic to a Lie group if [Formula: see text] is a nontrivial closed quasi-Yamabe soliton. Next, we consider an almost [Formula: see text]-cosymplectic manifold admitting a nontrivial almost quasi-Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector filed. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector filed, we also obtain two results. Finally, for a closed almost quasi-Yamabe soliton on compact [Formula: see text]-cosymplectic manifolds, we prove that it is trivial if [Formula: see text] is nonnegative, where [Formula: see text] is the scalar curvature.

scholarly journals SOME TYPES OF η-RICCI SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS

2018 ◽  
Vol 33 (2) ◽  
pp. 217
Author(s):  
Abhishek Singh ◽  
Shyam Kishor
Keyword(s):  
Vector Field ◽  
Einstein Manifold ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Sasakian Manifolds ◽  
Potential Vector ◽  
3 Dimensional ◽  
Potential Vector Field

In this paper we study some types of  η-Ricci solitons on Lorentzianpara-Sasakian manifolds and we give an example of  η-Ricci solitons on 3-dimensional Lorentzian para-Sasakian manifold. We obtain the conditions of  η-Ricci soliton on ϕ-conformally flat, ϕ-conharmonically flat and ϕ-projectivelyflat Lorentzian para-Sasakian manifolds, the existence of η-Ricci solitons implies that (M,g) is  η-Einstein manifold. In these cases there is no Ricci solitonon M with the potential vector field

scholarly journals Geometry of α-Cosymplectic Metric as ∗-Conformal η-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2189
Author(s):  
Pengfei Zhang ◽  
Yanlin Li ◽  
Soumendu Roy ◽  
Santu Dey
Keyword(s):  
Conformal Killing ◽  
Soliton Equation ◽  
Potential Vector ◽  
Research Article ◽  
Cosymplectic Manifolds ◽  
Metric Connection ◽  
Gradient Type ◽  
Yamabe Solitons ◽  
Yamabe Soliton ◽  
Potential Vector Field

The outline of this research article is to initiate the development of a ∗-conformal η-Ricci–Yamabe soliton in α-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of α-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from ∗-conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field’s conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional α-cosymplectic metric as a ∗-conformal η-Ricci–Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.

Ricci almost solitons and contact geometry

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Amalendu Ghosh
Keyword(s):  
Vector Field ◽  
Contact Manifold ◽  
Ricci Soliton ◽  
Jacobi Field ◽  
Reeb Vector ◽  
Potential Vector ◽  
Reeb Vector Field ◽  
Rigidity Results ◽  
Parallel Ricci Tensor ◽  
Potential Vector Field

Abstract We prove that on a K-contact manifold, a Ricci almost soliton is a Ricci soliton if and only if the potential vector field V is a Jacobi field along the Reeb vector field ξ. Then we study contact metric as a Ricci almost soliton with parallel Ricci tensor. To this end, we consider Ricci almost solitons whose potential vector field is a contact vector field and prove some rigidity results.

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

2019 ◽  
Vol 17 (1) ◽  
pp. 874-882 ◽  
Author(s):  
Xinxin Dai ◽  
Yan Zhao ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Ricci Soliton ◽  
Contact Transformation ◽  
Kenmotsu Manifold ◽  
Potential Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Dimension 2 ◽  
Potential Vector Field

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.

scholarly journals Locally homogeneous non-gradient quasi-Einstein 3-manifolds

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Alice Lim
Keyword(s):  
Vector Field ◽  
Lie Group ◽  
Compact Manifold ◽  
Einstein Metrics ◽  
Potential Vector ◽  
Compact Quotient ◽  
Locally Homogeneous ◽  
Potential Vector Field ◽  
The Way

Abstract In this paper, we classify the compact locally homogeneous non-gradient m-quasi Einstein 3- manifolds. Along the way, we also prove that given a compact quotient of a Lie group of any dimension that is m-quasi Einstein, the potential vector field X must be left invariant and Killing. We also classify the nontrivial m-quasi Einstein metrics that are a compact quotient of the product of two Einstein metrics. We also show that S1 is the only compact manifold of any dimension which admits a metric which is nontrivially m-quasi Einstein and Einstein.

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