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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…
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…
In the paper, we study complete almost Ricci solitons using the concepts and methods of geometric dynamics and geometric analysis. In particular, we characterize Einstein manifolds in the class of complete almost Ricci solitons. Then, we…
In this note, we present a construction method and an explicit example of nongradient (expanding or indefinite) Ricci almost soliton in a warped product. Moreover, we show a rigidity result for the Gaussian soliton.
The aim of this paper is to investigate some integral formulas for compact gradient $h$-almost Ricci-Bourguignon solitons. Consequently, we generalize the results previously ob tained for Ricci almost solitons. Moreover, we prove that a…
We study the modified Ricci solitons as a new class of Einstein type metrics that contains both Ricci solitons and $n$-quasi-Einstein metrics. This class is closely related to the construction of the Ricci solitons that are realised as…
In this paper, we revisit the study of almost Ricci-Bourguignon solitons by clarifying their position in the broader context of Einstein-type metrics. Motivated by known rigidity results for compact almost Ricci solitons, we aim to identify…
In this paper we study gradient Ricci-Harmonic soliton with structure of warped product manifold. We obtain some triviality results for the potential function, warping function and the harmonic map which reaches maximum or minimum. In order…
Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci tensor of such a soliton is the vertical component of both B-metrics multiplied by a…
We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear…
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…
We introduce the concept {\it $h$-almost Ricci soliton} which extends naturally the {\it almost Ricci soliton} by Pigola-Rigoli-Rimoldi-Setti and show that a compact nontrivial $h$-almost Ricci soliton of dimension no less than three with…
We present the necessary and sufficient conditions for constructing gradient Ricci almost solitons that are realized as warped products. This will be done by means of Bishop-O'Neill's formulas and a particular study of Riemannian manifolds…
The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton then it is isometric to a…
The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighborhood of any point where the gradient of the potential function is non-null. In…
We prove some results for the solitons of the Ricci-Bourguignon flow, generalizing corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci-Bourguignon $almost$ solitons…
We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.
This paper provides a study of algebraic Ricci solitons in the pseudo-Riemannian case. In the Riemannian case, all nontrivial homogeneous algebraic Ricci solitons are expanding algebraic Ricci solitons. In this paper, we obtain a steady…
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…
We describe the structure of the Ricci tensor on a locally homogeneous Lorentzian gradient Ricci soliton. In the non-steady case, we show the soliton is rigid in dimensions three and four. In the steady case, we give a complete…