Related papers: Some geometric analysis on generic Ricci solitons

We give a result estimating the dimension of the Lie algebra of Killing vector fields on an irreducible non-trivial gradient Ricci soliton. Then we study the structure of this manifold when the maximal dimension is attained. There are local…

In this paper, we study the gradient Ricci soliton equation on a complete Riemannian manifold. We show that under a natural decay condition on the Ricci curvature, the Ricci soliton is Ricci-flat and ALE.

In this work, we study metrics which are both homogeneous and Ricci soliton. If there exists a transitive solvable group of isometries on a Ricci soliton, we show that it is isometric to a solvsoliton. Moreover, unless the manifold is flat,…

In this paper, we continue to study the generalized Ricci flow. We give a criterion on steady gradient Ricci soliton on complete and noncompact Riemannian manifolds that is Ricci-flat, and then introduce a natural flow whose stable points…

We mainly study 3-dimensional complete gradient Ricci solitons with positive sectional curvature, whose scalar curvature attains its maximum at some point. In section 2, we estimate the area growth of level sets and the volume growth of…

We consider Ricci flow on two classes of nilpotent Lie groups that generalize the three-dimensional Heisenberg group: the higher-dimensional classical Heisenberg groups, and the groups of real unitriangular matrices. Each group is known to…

This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to…

We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat…

The purpose of the present paper is to study semi-generalized recurrent, semi-generalized Ricci recurrent and conformal Ricci soliton on (LCS)n-manifold.

A lower-bound estimate of injectivity radius for complete Riemannian manifolds is discussed in a pure geometric viewpoint and is applied to study tangent cones at infinity of certain gradient Ricci solitons. We also study the asymptotic…

We study the geometry at infinity of expanding gradient Ricci solitons of dimension greater than two with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a cone structure at infinity.

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…

We construct new examples of various solitons as warped products. There are classes of complete Ricci almost solitons and complete Ricci-Bourguignon solitons that can be explicitly described in terms of elementary functions.

Any homogeneous expanding Ricci soliton is known to be isometric to a Lie subgroup of the solvable part of the Iwasawa decomposition associated with a symmetric space of non-compact type, with the metric induced as a submanifold. In this…

In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be…

We study the properties of LP-Sasakian manifolds endowed with generalized $% \eta -$Ricci solitons associated to the general connection. Finally, the existence of such solitons on a 4-dimensional LP-Sasakian manifold is proved by…

This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes…

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…

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…

The concept of the Ricci soliton was introduced by Hamilton. Ricci soliton is defined by vector field and it's a natural generalization of Einstein metric. We have shown earlier that the vector field of Ricci soliton is an infinitesimal…