Related papers: On the Geometry of complete Ricci Solitons

We introduce a class of overdetermined systems of partial differential equations of finite type on (pseudo)-Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For…

We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.

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.

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…

We study $3$-dimensional Ricci solitons which project via a semi-conformal mapping to a surface. We reformulate the equations in terms of parameters of the map; this enables us to give an ansatz for constructing solitons in terms of data on…

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 $\mathds{S}^3$,…

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…

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…

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.

We study some properties of a $3$-dimensional manifold with a diagonal Riemannian metric as an almost $\eta$-Ricci soliton from the following points of view: under certain assumptions, we determine the potential vector field if $\eta$ is…

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…

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.

We consider three- and four-dimensional pseudo-Riemannian generalized symmetric spaces, whose invariant metrics were explicitly described in [15]. While four-dimensional pseudo-Riemannian generalized symmetric spaces of types A, C and D are…

In this paper a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the set-ups of…

In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on $S^n$, $\R{n}$ and $\R{}\times S^{n-1}$ are,…

Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and $\eta$-Ricci and $\eta$-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady,…

Some aspects of the multidimensional soliton geometry are considered.

Let $\overline{M}^{n+1}$ be a semi-Riemannian manifold of constant sectional curvature, and endowed with a conformal vector field . Consider a Riemannian manifold $M^n$, isometrically immersed into $\overline{M}^{n+1}$. With these…

In this paper, we study conformal Ricci solitons and conformal gradient Ricci solitons on generalized ($\kappa,\mu$)-space forms. The conditions for the solitons to be shrinking, steady, and expanding are derived in terms of conformal…

This paper studies gradient almost Ricci-harmonic soliton with respect to a fixed metric. We rely on analytic techniques to estabilish some basic elliptic and integral equations for the structure of almost Ricci-harmonic soliton which…