Results 41 to 50 of about 387 (181)

On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor

, 2020
In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat gradient steady Ricci solitons.
Cao, Huai-Dong, Yu, Jiangtao
core   +3 more sources

Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold

Karpatsʹkì Matematičnì Publìkacìï, 2019
First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding ...
A. Ghosh
doaj   +1 more source

On Bach-flat gradient shrinking Ricci solitons

, 2012
In this paper, we classify n-dimensional (n>3) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat hence a finite
Chen, Qiang, Cao, Huai-Dong, Huai-dong Cao, Qiang Chen   +3 more
core   +3 more sources

Compactness theorems for gradient Ricci solitons [PDF]

Journal of Geometry and Physics, 2006
21pages
openaire   +3 more sources

A Gradient Bound for the Allen-Cahn Equation Under Almost Ricci Solitons [PDF]

Sahand Communications in Mathematical Analysis
In this paper, we consider positive solutions for the Allen-Cahn equation\begin{equation*}\Delta u+\left(1-u^{2}\right)u=0,\end{equation*}on an almost Ricci soliton   without a boundary. Firstly, using volume comparison Theorem and Sobolev inequality, we
Sakineh Hajiaghasi, Shahroud Azami
doaj   +1 more source

Soliton-Type Equations on a Riemannian Manifold

Mathematics, 2022
We study some particular cases of soliton-type equations on a Riemannian manifold. We give an estimation of the first nonzero eigenvalue of the Laplace operator and provide necessary and sufficient conditions for the manifold to be isometric to a sphere.
Nasser Bin Turki, Adara M. Blaga, Sharief Deshmukh   +2 more
doaj   +1 more source

Remarks on the Warped Product Structure from the Hessian of a Function

Mathematics, 2018
The warped product structure of a gradient Yamabe soliton and a Ricci soliton with a concircular potential field is proved in another way.
Jong Ryul Kim
doaj   +1 more source

Conformal η-Ricci Solitons on Riemannian Submersions under Canonical Variation

Axioms, 2022
This research article endeavors to discuss the attributes of Riemannian submersions under the canonical variation in terms of the conformal η-Ricci soliton and gradient conformal η-Ricci soliton with a potential vector field ζ.
Mohd. Danish Siddiqi, Ali Hussain Alkhaldi, Meraj Ali Khan, Aliya Naaz Siddiqui   +3 more
doaj   +1 more source

A note on gradient $\ast$-Ricci Solitons

Mathematical Sciences and Applications E-Notes, 2020
In the offering exposition we characterize $(k,\mu)'$- almost Kenmotsu $3$-manifolds admitting gradient $\ast$-Ricci soliton. It is shown that a $(k,\mu)'$- almost Kenmotsu manifold with $k<-1$ is admitting a gradient $\ast$-Ricci soliton, either the soliton is steady or the manifold is locally isometric to a rigid gradient Ricci ...
openaire   +3 more sources

η-Ricci–Yamabe Solitons along Riemannian Submersions

Axioms, 2023
In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the η-Ricci–Yamabe soliton (η-RY soliton) with a potential field.
Mohd Danish Siddiqi, Fatemah Mofarreh, Mehmet Akif Akyol, Ali H. Hakami   +3 more
doaj   +1 more source