Related papers: Back to almost Ricci solitons
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…
In this article, we consider an orthogonal decomposition of the traceless part of the Ricci tensor of a compact Riemannian manifold and study its application to the geometry of compact almost Ricci solitons. In addition, we consider an…
On an $n$-dimensional complete manifold $M$, consider an $h$-almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove that if the manifold is Bach-flat and $dh/du>0$, then the manifold $M$ is either…
Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $\Pi$-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of…
We study several classes of Riemannian manifolds which are defined by imposing a certain condition on the Ricci tensor. We consider the following cases: Ricci recurrent, Cotton, quasi Einstein and pseudo Ricci symmetric condition. Such…
We present a general numerical method for investigating prescribed Ricci curvature problems on toric K\"ahler manifolds. This method is applied to two generalisations of Einstein metrics, namely Ricci solitons and quasi-Einstein metrics. We…
In Riemannian geometry, Ricci soliton inequalities are an important field of study that provide profound insights into the geometric and analytic characteristics of Riemannian manifolds. An extensive study of Ricci soliton inequalities is…
A Ricci soliton is a natural generalization of an Einstein metric. On a pseudo-Riemannian manifold (M, g), it is defined by : $LX g + \r{ho} = {\lambda} g, where X is a smooth vector field on M , LX denotes the Lie derivative in the…
The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is…
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…
In this paper, we completely classify almost Yamabe solitons on hypersurfaces in Euclidean spaces arisen from the position vector field. Some results of almost Yamabe solitons with a concurrent vector field and almost Yamabe solitons on…
The aim of this article is to study the Riemann soliton and gradient almost Riemann soliton on certain class of almost Kenmotsu manifolds. Also some suitable examples of Kenmotsu and $(\kappa,\mu)'$-almost Kenmotsu manifolds are constructed…
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.
This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given…
The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci…
In this paper, we study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows…
B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to…
We study deformations of shrinking Ricci solitons on a compact manifold M, generalising the classical theory of deformations of Einstein metrics. Using appropriate notions of twisted slices S_f inside the space of all Riemannian metrics on…
We consider almost Riemann and almost Ricci solitons in a $D$-homothetically deformed Kenmotsu manifold having as potential vector field a gradient vector field, a solenoidal vector field or the Reeb vector field of the deformed structure,…
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…