On modifying the gravitational action by addition of higher-derivative terms of curvature, it is obtained that the Ricci scalar behaves as a physical field as well as a geometrical field. Riccion is a particle giving the physical aspect of the Ricci scalar curvature. Here, it is probed about the possibility of riccion being a candidate for cosmic cold dark matter. PACS nos.: 98.80-k; 95.30 C.

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

We show that on a compact Riemannian manifold with boundary there exists u ∈ C(M) such that, u|∂M ≡ 0 and u solves the σk-Ricci problem. In the case k = n the metric has negative Ricci curvature. Furthermore, we show the existence of a complete conformally related metric on the interior solving the σk-Ricci problem. By adopting results of [14], we show an interesting relationship between the co...

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

A Sasakian structure S=(;;;;g) on a manifold M is called positive if its basic rst Chern class c 1 (F) can be represented by a positive (1;1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This allows us by example to give a comple...

The object of the present paper is to characterize K-contact Einstein manifolds satisfying the curvature condition R · C = Q(S,C), where C is the conformal curvature tensor and R the Riemannian curvature tensor. Next we study K-contact Einstein manifolds satisfying the curvature conditions C ·S = 0 and S ·C = 0, where S is the Ricci tensor. Finally, we consider K-contact Einstein manifolds sati...

Let M be a compact embedded submanifold with parallel mean curvature vector and positive Ricci curvature in the unit sphere Sn+p (n≥ 2, p ≥ 1). By using the Sobolev inequalities of P. Li (1980) to Lp estimate for the square length σ of the second fundamental form and the norm of a tensor φ, related to the second fundamental form, we set up some rigidity theorems. Denote by ‖σ‖p the Lp norm of σ...

In this paper, we construct local and global solutions to the K\"ahler-Ricci flow from a non-collapsed K\"ahler manifold with curvature bounded below. Combines mollification technique of McLeod-Simon-Topping, show that Gromov-Hausdorff limit sequence complete noncompact manifolds orthogonal bisectional Ricci below is homeomorphic complex manifold. We also use it study structure nonnegative curv...

We show that the first betti number b1 (0) = d im H 1(0, !R) of a compact Riemannian orbifold 0 with Ricci curvature Ric(O ) ~ -(n 1)k and d iameter diam(O) :5 D is bounded above by a constant r (n, kD2 ) ~ 0 , depending only on dimension , curvature and diameter. In the case when t he orbi fold has nonnegative Ricci curvature, we show that the b1 (0) is bounded above by the dimension dim 0 , a...

We define a notion of a measured length space X having nonnegative N -Ricci curvature, for N ∈ [1,∞), or having ∞-Ricci curvature bounded below by K, for K ∈ R. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric space P2(X) of probability measures. We show that these properties are preserved under measured Gromov-Hausdorff limits...