Related papers: Homogeneous Ricci solitons
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…
In this paper, we have proved that if a complete conformally flat gradient shrinking Ricci soliton has linear volume growth or the scalar curvature is finitely integrable and also the reciprocal of the potential function is subharmonic,…
Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are…
It is well known that every compact simple Lie group G admits an Einstein metric that is invariant under the independent left and right actions of G. In addition to this bi-invariant metric, with G x G symmetry, it was shown by D'Atri and…
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…
We develop a framework inspired by Lauret's "bracket flow" to study the generalized Ricci flow, as introduced by Streets, on discrete quotients of Lie groups. As a first application, we establish global existence on solvmanifolds in…
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the…
We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively. After a review of some classical results, we use the Gleason-Iwasawa-Montgomery-Yamabe-Zippin structure…
In this paper we prove that given a smoothly conformally compact metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact. We adapt recent results of Schn\"urer, Schulze and Simon to prove a…
In this paper, I computed the second variation formula of the generalized Einstein-Hilbert functional and prove that a Bismut-flat, Einstein manifold is linearly stable under some curvature assumption. In the last part of the paper, I prove…
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…
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…
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…
We use analytical and numerical methods to investigate the equations for cohomogeneity one shrinking gradient Ricci solitons. We show the existence of a winding number for this system around the subvariety of phase space corresponding to…
It is known that all left-invariant pseudo-Riemannian metrics on $H_3$ are algebraic Ricci solitons. We consider generalizations of Riemannian $H$-type, namely pseudo$H$-type and $pH$-type. We study algebraic Ricci solitons of…
Symmetric symplectic spaces of Ricci type are a class of symmetric symplectic spaces which can be entirely described by reduction of certain quadratic Hamiltonian systems in a symplectic vector space. We determine, in a large number of…
We ask a general question: what are locally homogeneous compact pseudo-Riemannian Einstein manifolds? We show that any standard compact Clifford-Klein form of a simple non-compact Lie group admits at least one Einstein metric. We conjecture…
Ricci soliton contact metric manifolds with certain nullity conditions have recently been studied by Ghosh and Sharma. Whereas the gradient case is well-understood, they provided a list of candidates for the nongradient case.These…
We show that a complete gradient Ricci soliton $(M^n,\,g)$ with constant scalar curvature and a non-parallel closed conformal vector field is isometric to either the Euclidean space, or an Euclidean sphere, or negatively Einstein warped…
In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant…