In this article, normal paracontact metric space forms are investigated on W_0-curvature tensor. Characterizations of obtained Special curvature conditions established with the help Riemann, Ricci, concircular tensors discussed With these conditions, important characterizations obtained.

Let M be a real hypersurface of complex space form n ( c ) $M^n(c)$ , ≠ 0 $c\ne 0$ . Suppose that the structure vector field ξ is an eigen Ricci tensor S, S = β $S\xi =\beta \xi$ being function. We study on M, gradient pseudo-Ricci soliton g f λ μ $M,g,f,\lambda ,\mu$ extended concept soliton, closely related to pseudo-Einstein hypersurfaces. When ≥ 3 $n\ge 3$ we show Hopf hypersurface.

휂-Ricci solitons on Lorentzian 훽-Kenmotsu manifold are considered an manifolds satisfying certain curvature Conditions, R(ξ,X).S=0, S(ξ,X).R=0, W2(ξ,X).S=0,S(ξ,X).W2=0 We proved that in β-Kenmotsu (M,φ,ξ,η,푔). Then the existence of implies M is Einstein and if Ricci tensor satisfies, then steady. If condition 휇=0, 휆=0, which shows 휆is steady

In this article, the behavior of C(α)-manifold satisfying conditions R(X,Y)W∗ = 0,W∗ (X,Y)R (X,Y)Z˜ 0, W∗ (X,Y)S 0 and (X,Y)C˜ on M−projective curvature tensor is investigated. The C(α)−Manifold characterized according to these states tensor. Here, ,R,S,Z˜ C˜ are M−projective, Riemann, Ricci, concircular quasiconformal tensors

Considering the evolution equations of parabolic type on a non-compact Einstein manifold $(\mathcal M,g)$ with negative Ricci curvature tensor, we establish results existence, uniqueness time-periodic (on time half-axis) and almost periodic

Plasma toroidal metric singularities in helical devices and tokamaks, giving rise to magnetic surfaces inside the plasma devices are investigated in two cases. In the first we consider the case of a rotational plasma on an helical device with circular cross-section and dissipation. In this case singularities are shown to place a Ricci scalar curvature bound on the radius of the surface where th...

We show that there exists a 2-parameter family F of Riemannian metrics on the twistor space Z of a positive quaternion Kähler manifold M having the following properties : (1) the family F is closed under the operation of making the convex sums, (2) the Ricci map g 7→ Ric(g) sends the family F to itself, (3) the family F contains the scalings of a Kähler-Einstein metric of Z. We show that the Ri...

A smooth closed manifold M is called almost Ricci-flat if $$\begin{aligned} \inf _g||\text {Ric}_g||_\infty \cdot \text {diam}_g(M)^2=0 \end{aligned}$$ where $$\text {Ric}_g$$ and {diam}_g$$ , respectively, denote the Ricci tensor diameter of g runs over all Riemannian metrics on M. By using Kummer-type method, we construct a nonspin 5-manifold which simply connected. It minimal volume vanishes...

The aim of this project is to introduce the basics of Hamilton’s Ricci Flow. The Ricci flow is a pde for evolving the metric tensor in a Riemannian manifold to make it “rounder”, in the hope that one may draw topological conclusions from the existence of such “round” metrics. Indeed, the Ricci flow has recently been used to prove two very deep theorems in topology, namely the Geometrization and...

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.