Related papers: Ricci solitons and concurrent vector fields
We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition,…
We show for a complete noncompact steady Ricci soliton that there exists a sequence {x_i} of points tending to infinity such that |Rc|(x_i) limits to zero.
In this paper, we study the existence of harmonic and bi-harmonic maps into Riemannian manifolds admitting a conformal vector field, or a nontrivial Ricci solitons.
We develop a method for constructing complete gradient Ricci solitons realized as fiber bundles endowed with warped metrics, and we establish necessary and sufficient conditions for their existence. As an application, we present new…
In this paper, we first show that a complete shrinking breather with Ricci curvature bounded from below must be a shrinking gradient Ricci soliton. This result has several applications. First, we can classify all complete $3$-dimensional…
In the present paper we study $\eta$-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider $\eta$-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study…
The prescribed Ricci curvature problem consists in finding a Riemannian metric $g$ on a manifold $M$ such that the Ricci curvature of $g$ equals a given $(0,2)$-tensor field $T$. We survey the recent progress on this problem in the case…
In this survey article, we discuss some topics on self-similar solutions to the Ricci flow and the mean curvature flow. Self-similar solutions to the Ricci flow are known as Ricci solitons. In the first part of this paper we discuss a lower…
Consider a compact Lie group $G$ and a closed subgroup $H<G$. Suppose $\mathcal M$ is the set of $G$-invariant Riemannian metrics on the homogeneous space $M=G/H$. We obtain a sufficient condition for the existence of $g\in\mathcal M$ and…
In this article, we study mixed Killing vector fields, defined by the condition $L_V L_V g = f\, L_V g$, on the Cigar Ricci--Bourguignon soliton. While conformal vector fields are always mixed Killing, the converse fails in flat and open…
In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold $\varrg$, unifying various particular cases recently studied in the literature, such as gradient Ricci solitons, Yamabe solitons and quasi-Einstein…
It is shown that on compact $Spin(7)$--manifold with exterior derivative of the Lee form lying in the Lie algebra $spin(7)$ the curvature $R$ of the $Spin(7)$--torsion connection $R\in S^2\Lambda^2$ with vanishing Ricci tensor if and only…
In this paper, it is proved that a connected 3-dimensional Riemannian manifold or a closed connected semi-Riemannian manifold $M^n$($n>1$) admitting a projective vector field with a non-linearizable singularity is projectively flat.
We completely classify the algebraic Ricci solitons of four-dimensional pseudo-Riemannian generalized symmetric spaces.
Let $(M, g, f)$ be a $5$-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= \lambda g$, where $\text{Ric}$ is the Ricci tensor and $\nabla^2f$ is the Hessian of the potential function $f$. We…
The goal of this article is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these…
In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume…
We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.
Ricci solitons on Finsler spaces, previously developed by the present authors, are a generalization of Einstein spaces, which can be considered as a solution to the Ricci flow on compact Finsler manifolds. In the present work it is shown…
In this paper we introduce the notion of rigidity for harmonic-Ricci solitons and we provide some characterizations of rigidity, generalizing some known results for Ricci solitons. In the compact case we are able to deal with not…