Related papers: On a Class of Gradient Almost Ricci Solitons

I In this paper, first we study a complete smooth metric measure space $(M^n,g, e^{-f}dv)$ with the ($\infty$)-Bakry-\'Emery Ricci curvature $\textrm{Ric}_f\ge \frac a2g$ for some positive constant $a$. It is known that the spectrum of the…

Applying a well known result for attracting fixed points of biholomorphisms \cite{RR, V}, we observe that one immediately obtains the following result: if $(M^n,g)$ is a complete non-compact gradient K\"ahler-Ricci soliton which is either…

We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some…

We first show that any $4$-dimensional non-Ricci-flat steady gradient Ricci soliton singularity model must satisfy $|Rm|\leq cR$ for some positive constant $c$. Then, we apply the Hamilton-Ivey estimate to prove a quantitative lower bound…

In this paper we consider a perturbation of the Ricci solitons equation proposed by J. P. Bourguignon in \cite{jpb1}. We show that these structures are more rigid then standard Ricci solitons. In particular, we prove that there is only one…

In this paper, we consider a left-invariant Riemannian metric $g$ on the Lie group $F^4$. We classify Ricci solitons on $(F^4,g)$ and show that all such solitons are expanding and non-gradient. Moreover, we study the existence of harmonic…

Gradient Ricci almost solitons were introduced by Pigola, Rigoli, Rimoldi and Setti. They are defined as solitons except that the metric coefficient is required to be a smooth function rather than a constant. It is shown that any almost…

We prove that a four-dimensional gradient shrinking Ricci soliton with $\delta W^{\pm}=0$ is either Einstein, or a finite quotient of $S^3\times\mathbb{R}$, $S^2\times\mathbb{R}^2$ or $\mathbb{R}^4$. We also prove that a four-dimensional…

In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a K\"ahler model. The first theorem could be considered as a rigidity result for the K\"ahler-Ricci soliton structure on $\mathbb{S}^2\times…

Considering pseudo-Riemannian $g$-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure…

In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product $\mathbb{R}\times N^{n-1}$, or globally conformally equivalent to the Euclidean space $\mathbb{R}^{n}$…

We consider three- and four-dimensional pseudo-Riemannian generalized symmetric spaces, whose invariant metrics were explicitly described in [15]. While four-dimensional pseudo-Riemannian generalized symmetric spaces of types A, C and D are…

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 study hypersurfaces in the product spaces $\mathbb{Q}_{\epsilon}^3 \times \mathbb{R}$ for which the tangential component $T$ of the vector field $\frac{\partial}{\partial t}$ is a principal direction, where…

The prime object of this article is to study the perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity, when $\eta$-Ricci solitons, gradient $\eta$-Ricci solitons, gradient Einstein Solitons and gradient $m$-quasi Einstein solitons are…

We prove that there exists a gradient expanding Ricci soliton asymptotic to any given cone over the product of a round sphere and a Ricci flat manifold. In particular we obtain asymptotically conical expanding Ricci solitons with positive…

We show that a three-dimensional steady gradient Ricci soliton which is asymptotic to the Bryant soliton in a suitable sense must be isometric to the Bryant soliton.

In this paper, we establish a compactness theorem for gradient Ricci solitons with scalar curvature bounds and uniform lower bounds of harmonic coordinates. Our approach is to bootstrap regularity in harmonic coordinates by exploiting the…

A generalization of Ricci-like solitons with torse-forming potential, which is a constant multiple of the Reeb vector field, is studied. The conditions under which these solitons are equivalent to almost Einstein-like metrics are given.…

Conformal Ricci solitons are self similar solutions of the conformal Ricci flow equation. This paper deals with the study of conformal Ricci solitons within the framework of warped product manifolds which extends the notion of usual…