Abstract The Ricci curvature criterion is used for the investigation of the relative instability of several configurations of N-body gravitating systems. It is shown, that the systems with double massive centers are more unstable than the homogeneous systems and those with one massive center. In general this shows the efficiency of the Ricci curvature method introduced by Gurzadyan and Kocharya...

We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path-connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the threeball) is contractible. As an application, using results of Maximo, Nunes, and Smith [MNS], we show the existence of properly embedd...

We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k-fold connected sum of S × S admit Sasakian metrics with positive Ricci curvature for all k. Furthermore, a formula for computing the diffeomorphism types is given and tables are presented for dimensions 7 and...

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.

1 Introduction The uniformalization of Kähler manifold has been an important topic in geometry for long. The famous Frankel Conjecture states: Compact n-dimensional Kähler Manifolds of Positive Bisectional Curvature are Bi-holomorphic to P n C. [10] by using stable harmonic maps in the context of Kähler geometry. Actually, Mori proved the Harthshorne Conjecture: Every irreducible n-dimensional ...

In this paper, we study the dilation limit of solutions to the Ricci flow on manifolds with nonnegative curvature operator. We first show that such a dilation limit must be a product of a compact ancient Type I solution of the Ricci flow with flat factors. Then we show under the Type I normalized Ricci flow, the compact factor has a subsequence converge to a Ricci soliton.

In this short paper we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result Böhm and Wilking have for dimensions twelve and above. Moreover, the manifolds constructed here are...

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξ and its covariant derivative ∇̃ξ and determine relations between the decompositions of ξ ⊗ ξ, ∇̃ξ and R. We pay particular attention to the...

This paper investigates the Olivier-Ricci curvature (ORC) characteristics of a low-power wireless network deployment. We quantitatively analyze how the OCR varies among different channels of a IEEE 802.15.4-based network heavily influenced by external interference. And, finally, verify the correlation between the topology curvature of network graphs and the performance of time-scheduled protoco...

Let (M, g) be a complete non compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. Extending our techniques developed in [8], we prove that the universal cover M̃ of M is biholomorphic to Cn provided either that (M, g) has average quadratic curvature decay, or M supports an eternal solution to the Kähler-Ricci flow with non-negative and uniformly bounded holomo...