Related papers: Some geometric analysis on generic Ricci solitons
The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three dimensional generic shrinking Ricci soliton is given by quotients of either $\mathds{S}^3$,…
We classify and expose all the gradient Ricci solitons on complete surfaces, open or closed, with curvature bounded below, and possibly with a discrete set of cone-like singular points that arise naturally. We give a precise qualitative…
The objective of the present paper is to study the $\eta$-Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha,\beta)$. There are discussed Ricci and $\eta$-Ricci solitons with generalized…
We completely describe paracontact metric three-manifolds whose Reeb vector field satisfies the Ricci soliton equation. While contact Riemannian (or Lorentz\-ian) Ricci solitons are necessarily trivial, that is, $K$-contact and Einstein,…
The geometric flow theory and its applications turned into one of the most intensively developing branches of modern geometry. Here, a brief introduction to Finslerian Ricci flow and their self-similar solutions known as Ricci solitons are…
In this paper, we characterize the Ricci soliton equations on the Poincar\'e upper half plane . First we classify all Ricci soliton and Ricci Bourguignon soliton in the half plane of Poincar\'e and after we generalize those equations in…
We describe three-dimensional Lorentzian homogeneous Ricci solitons, showing that all types (i.e. shrinking, expanding and steady) exist. Moreover, all non-trivial examples have non-diagonalizable Ricci operator with one only eigenvalue.
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 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 $N(k)$-contact metric manifolds and/or $(k,\mu)$-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with $V$ pointwise collinear with the structure vector field $\xi $ are studied.
I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used 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…
We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not…
The present paper deals with the study of Ricci solitons on invariant and anti-invariant submanifolds of $(LCS)_n$-manifolds with respect to Riemannian connection as well as quarter symmetric metric connection.
As a generalization of Einstein manifolds, the nearly quasi-Einstein manifolds and pseudo quasi-Einstein manifolds are both interesting and useful in studying the general relativity. In this paper, we study the extended quasi-Einstein…
We study almost Riemann solitons and almost Ricci solitons in an $(\alpha,\beta)$-contact metric manifold satisfying some Ricci symmetry conditions, treating the case when the potential vector field of the soliton is pointwise collinear…
We discuss the geometry of homogeneous Ricci solitons. After showing the nonexistence of compact homogeneous and noncompact steady homogeneous solitons, we concentrate on the study of left invariant Ricci solitons. We show that, in the…
In this note, we complete the classification of the geometry of non-compact two-dimensional gradient Ricci solitons. As a consequence, we obtain two corollaries: First, a complete two-dimensional gradient Ricci soliton has bounded…
In this note, we find a necessary condition on odd-dimensional Riemannian manifolds under which both of Sasakian structure and the generalised Ricci soliton equation are satisfied, and we give some examples.
We study metric structures on a smooth manifold (introduced in our recent works and called a weak contact metric structure and a weak K-structure) which generalize the metric contact and K-contact structures, and allow a new look at the…