In this paper we introduce notion of Ricci solitons in -para Kenmotsu manifold with semi -symmetric metric connection. We have found the relations between curvature tensor, tensors and scalar semi-symmetic connection.We proved that 3-dimensional connection is an -Einstein soliton defined on named expanding steady respect to value constant.It Conharmonically flat semi-symmetric manifold.

This review article has grown out of notes for the three lectures the second author presented during the XXIV-th Winter School of Geometry and Physics in Srni, Czech Republic, in January of 2004. Our purpose is twofold. We want give a brief introduction to some of the techniques we have developed over the last 5 years while, at the same time, we summarize all the known results. We do not give a...

We provide necessary and sufficient conditions for some particular couples ( g , ? ) of pseudo-Riemannian metrics affine connections to be statistical structures if we have gradient almost Einstein, Ricci, Yamabe solitons, or a more general type solitons on the manifold. In cases, establish formula volume manifold give lower an upper bound norm Ricci curvature tensor field.

We obtain some properties of a hyperbolic Ricci soliton with certain types potential vector fields, and we point out conditions when it reduces to trivial soliton. also study those submanifolds whose fields are the tangential components concurrent field on ambient manifold, in particular, show that totally umbilical is an Einstein manifold. prove if hypersurface Riemannian manifold constant cur...

In this paper, we study the uniformly strong convergence of Kähler-Ricci flow on a Fano manifold with varied initial metrics and smoothly deformed complex structures. As an application, prove uniqueness solitons in sense diffeomorphism orbits. The result generalizes Tian-Zhu’s theorem for compact manifold, it is also generalization Chen-Sun’s Kähler-Einstein metric

We introduce an evolution equation which deforms metrics on 3-manifolds with sectional curvature of one sign. Given a closed 3-manifold with an initial metric with negative sectional curvature, we conjecture that this flow will exist for all time and converge to a hyperbolic metric after a normalization. We shall establish a monotonicity formula in support of this conjecture. Note that in contr...

The purpose of this research is to investigate how a ρ-Einstein soliton structure on warped product manifold affects its base and fiber factor manifolds. Firstly, the pertinent properties solitons are provided. Secondly, numerous necessary sufficient conditions make examined. On gradient manifold, for making presented. manifolds admitting conformal vector field also considered. Finally, some sp...

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kahler ; in the non-exact Einstein-Weyl case with a Bianchi metr...

We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) hypo and half-flat evolution equations in higher dimensions. We use these equations to classify Einstein-Sasaki 5-manifolds of cohomogeneity one...

A horospherical variety is a normal $G$-variety such that connected reductive algebraic group $G$ acts with an open orbit isomorphic to torus bundle over rational homogeneous manifold. The projective manifolds of Picard number one are classified by Pasquier, and it turned out the automorphism groups all nonhomogeneous ones non-reductive, which implies they admit no K\"{a}hler--Einstein metrics....