Topic
Ricci decomposition
About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the Ricci tensor has been computed in infinite dimensional situations for the case of the central extension of loop groups and in the asymptotic behaviour of the Riemannian metric on free loop groups.
7 citations
TL;DR: In this paper, a lower bound of coarse Ricci curvature with respect to a random walk called an $$r$$ -step random walk was obtained for a metric measure space satisfying the curvaturedimension condition.
Abstract: In this paper,we investigate the coarse Ricci curvature on metric spaces with random walks. There exists no canonical random walk on metric space with a reference measure. However, we prove that a Bishop–Gromov inequality gives a lower bound of coarse Ricci curvature with respect to a random walk called an $$r$$
-step random walk. The lower bound does not coincide with the constant corresponding to curvature in Bishop–Gromov inequality. As a corollary, we obtain a lower bound of coarse Ricci curvature with respect to an $$r$$
-step random walk for a metric measure space satisfying the curvature-dimension condition. Moreover we give an important example, Heisenberg group, which does not satisfy the curvature-dimension condition for any constant but has a lower bound of coarse Ricci curvature. We also have an estimate of the eigenvalues of the Laplacian by a lower bound of coarse Ricci curvature.
7 citations
TL;DR: In this article, it was shown that all Riemannian spaces with this property are symmetric in the sense of Cartan [3] and that the first covariant derivative of Weyl's projective curvature tensor vanishes.
Abstract: Gy. Soos [1] and B. Gupta [2] have discussed the properties of Riemannian spaces V n ( n > 2) in which the first covariant derivative of Weyl's projective curvature tensor is everywhere zero; such spaces they call Protective-Symmetric spaces . In this paper we wish to point out that all Riemannian spaces with this property are symmetric in the sense of Cartan [3]; that is the first covariant derivative of the Riemann curvature tensor of the space vanishes. Further sections are devoted to a discussion of projective-symmetric af fine spaces A n with symmetric af fine connexion. Throughout, the geometrical quantities discussed will be as defined by Eisenhart [4] and [5].
7 citations
TL;DR: In this article, a new asymptotic one-sided and symmetric tensor norm is introduced, which can be considered as the minimal tensor norms on the category of separable C * -algebras with homotopy classes of asymPTotic homomorphisms as morphisms.
Abstract: We introduce a new asymptotic one-sided and symmetric tensor norm, the latter of which can be considered as the minimal tensor norm on the category of separable C
*-algebras with homotopy classes of asymptotic homomorphisms as morphisms. We show that the one-sided asymptotic tensor norm differs in general from both the minimal and the maximal tensor norms and discuss its relation to semi-invertibility of C
*-extensions.
7 citations
Posted Content•
TL;DR: In this paper, the authors proved a compactness result about Riemannian manifolds with an arbitrary pointwise pinched Ricci curvature tensor, where the Ricci tensor is a tensor tensor.
Abstract: In this paper, we proved a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.
7 citations