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 associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a...

In this paper, we study gradient Ricci expanding solitons (X, g) satisfying Rc = cg +Df, where Rc is the Ricci curvature, c < 0 is a constant, and Df is the Hessian of the potential function f on X . We show that for a gradient expanding soliton (X, g) with non-negative Ricci curvature, the scalar curvature R has at least one maximum point on X , which is the only minimum point of the potential...

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 associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a...

We study Ricci solitons in Lorentzian α-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian α-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if LV g + 2S is parallel, V is a given vector field then (g, V ) is Ricci soliton. Further, by virtue of this result Ricci solitons for (2n + 1)-dimensional Lor...

In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat steady solitons. More precisely, prove that any noncompact soliton with vanishing $D$-tensor is either Ricci-flat, or isometric Bryant soliton. Furthermore, proof extends shrinking case and expanding as well.

The aim of this paper is to study a contact Riemannian submersion ? : M B between almost metric manifolds such that its total space admits an ??Ricci soliton. Here, we obtain some necessary conditions for which any fiber and the manifold are soliton, Ricci generalized quasi-Einstein, ??Einstein or Einstein. Finally, equipped with torqued vector field give characterizations ?.

Let $F$ be a left invariant Randers metric on simply connected nilpotent Lie group $N$, induced by Riemannian ${\hat{\textbf{\textit{a}}}}$ and vector field $X$ which is $I_{\hat{\textbf{\textit{a}}}}(M)$-invariant. If the Ricci flow equation has unique solution then, $(N,F)$ soliton if only semialgebraic soliton.

Our goal in this paper is to obtain further information about the curvature of gradient shrinking Ricci solitons. This is important for a better understanding and ultimately for the classification of these manifolds. The classification of gradient shrinkers is known in dimensions 2 and 3, and assuming locally conformally flatness, in all dimensions n ≥ 4 (see [14, 13, 6, 15, 20, 12, 2]). Many o...

The goal of the current paper is to characterize $*$-$k$-Ricci-Yamabe soliton within framework on Kenmotsu manifolds. Here, we have shown nature and find scalar curvature when manifold admitting manifold. Next, evolved characterization vector field satisfies soliton. Also embellished some applications as torse-forming in terms Then, studied gradient $\ast$-$\eta$-Einstein yield Riemannian tenso...

In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume growth. The latter result can be viewed as an analog of the well-known theorem of Bishop that a complete noncompact Riemannian manifold with nonnegative Ricci cu...