Related papers: Invariant Solutions for Gradient Ricci Almost Soli…
We consider gradient Ricci solitons conformal to a $n$-dimensional pseudo-Euclidean space and we completely describe the most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary…
In this paper we study gradient Ricci-Harmonic soliton with structure of warped product manifold. We obtain some triviality results for the potential function, warping function and the harmonic map which reaches maximum or minimum. In order…
In this study, we provide some classifications for half-conformally flat gradient $f$-almost Ricci solitons, denoted by $(M, g, f)$, in both Lorentzian and neutral signature. First, we prove that if $||\nabla f||$ is a non-zero constant,…
We study the modified Ricci solitons as a new class of Einstein type metrics that contains both Ricci solitons and $n$-quasi-Einstein metrics. This class is closely related to the construction of the Ricci solitons that are realised as…
We study warped products semi-Riemannian Einstein manifolds. We consider the case in that the base is conformal to an n-dimensional pseudo Euclidean space and invariant under the action of an translation group. We provide all such solutions…
The aim of this paper is to study geometrical aspects of static spacetime admitting an almost gradient Ricci soliton. Among others, We first determine the conditions under which the base manifold of static spacetime possess an almost…
The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\big(M^n,\,g,\,X,\,\lambda\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\Bbb{S}^{n}$. As a consequence we obtain that every…
The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighborhood of any point where the gradient of the potential function is non-null. In…
We characterize Ricci almost solitons on semi-Riemannian warped products, considering the potential function to depend on the fiber or not. We show that the fiber is necessarily an Einstein manifold. As a consequence of our characterization…
We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci…
Let M be a smooth compact manifold without boundary. We consider two smooth Sub-Semi-Riemannian metrics on M. Under suitable conditions, we show that they are almost conformally isometric in an Lp sense. Assume also that M carries a…
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,…
We study gradient Ricci solitons warped products whose base is the Euclidean space. We show that the warping functions of these manifolds are invariant under the (n-1)-dimensional translation group. We characterize the potential function…
We present the necessary and sufficient conditions for constructing gradient Ricci almost solitons that are realized as warped products. This will be done by means of Bishop-O'Neill's formulas and a particular study of Riemannian manifolds…
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…
Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $\Pi$-manifolds are studied. It is proved that these objects have constant soliton coefficients. For the soliton under study is shown that the corresponding scalar…
We investigate K\"ahler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton…
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,…
Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci tensor of such a soliton is the vertical component of both B-metrics multiplied by a…
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…