In this article, a Ricci soliton and *-conformal are examined in the framework of trans-Sasakian three-manifold. beginning paper, it is shown that three-dimensional manifold type (?,?) admits where covariant derivative potential vector field V direction unit ? orthogonal to ?. It also demonstrated if structure functions meet ?2=?2, then constant multiple Furthermore, nature scalar curvature evo...

We study the properties of Ricci curvature ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between manifold and transverse characteristic foliation are investigated. In particular, sufficient conditions found under which ${\mathfrak{g}}$-manifold can be a soliton or gradient soliton. Finally, we obtain amazing (non-existenc...

We introduce and study a new type of soliton with potential Reeb vector field on Riemannian manifolds an almost paracontact structure corresponding to paracomplex structure. The special cases para-Einstein-like, para-Sasaki-like having torse-forming were considered. It was proved necessary sufficient condition for the manifold admit para-Ricci-like soliton, which is that para-Einstein-like. Exp...

Let (M, g) be a complete noncompact Riemannian manifold. In this paper, we derive a local gradient estimate for positive solutions to a simple nonlinear parabolic equation ∂u ∂t = ∆u+ au log u+ bu on M × [0,+∞), where a, b are two real constants. This equation is closely related to the gradient Ricci soliton. We extend the result of L. Ma (Journal of Functional Analysis 241 (2006) 374-382).

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 surface. A complete description of the soliton structures on all the 3-dimensional geometries is given, in particular, non-gradient solitons are found on ...

We consider a general notion of an almost Ricci soliton and establish some curvature properties for the case in which potential vector field is generalized geodesic or 2-Killing field. In this vein, we characterize trivial solitons.

Firstly we provide new characterizations for doubly warped product manifolds. Then consider several types of gradient solitons such as Riemann, Ricci, Yamabe and conformal, examine the effect a soliton on to its factor Finally, investigate concircularly flat conharmonically cases products.

Recently, Jablonski proved that, to a large extent, simply connected solvable Lie group endowed with left-invariant Ricci soliton metric can be isometrically embedded into the Iwasawa of non-compact symmetric space. Motivated by this result, we classify codimension one subgroups groups irreducible spaces type whose induced metrics are solitons. We also obtain classifications Damek-Ricci and gen...