Ricci decomposition

About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.

On Measure Contraction Property without Ricci Curvature Lower Bound

Abstract: Measure contraction properties M C P (K, N) are synthetic Ricci curvature lower bounds for metric measure spaces which do not necessarily have smooth structures. It is known that if a Riemannian manifold has dimension N, then M C P (K, N) is equivalent to Ricci curvature bounded below by K. On the other hand, it was observed in Rifford (Math. Control Relat. Fields 3(4), 467–487 2013) that there is a family of left invariant metrics on the three dimensional Heisenberg group for which the Ricci curvature is not bounded below. Though this family of metric spaces equipped with the Harr measure satisfy M C P (0,5). In this paper, we give sufficient conditions for a 2n+1 dimensional weakly Sasakian manifold to satisfy M C P (0, 2n + 3). This extends the above mentioned result on the Heisenberg group in Rifford (Math. Control Relat. Fields 3(4), 467–487 2013).

On a group approach to studying the Einstein and maxwell equations

Abstract: Based on the classical problem for decomposition of the tensor product of representations into irreducible components, which is considered in the elementary representation theory for orthogonal groups, a partial classification of the Einstein equations is carried out. A new class of Maxwell equations for relativistic electrodynamics is singled out and studied. Pointwise-irreducible decompositions for the energy-momentum and electromagnetic field tensors are obtained and a physical interpretation of the decomposition components is given.

Structure Tensor Image Filtering using Riemannian L_1 and L_∞ Center-of-Mass

Abstract: Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n), representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n) matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point) and L∞ center-of-mass (Riemannian circumcenter) can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i) structure tensor image denoising; (ii) anomaly detection in structure tensor images.

Pseudo-Riemannian Jacobi-Videv Manifolds

Abstract: We exhibit several families of Jacobi-Videv pseudo-Riemannian manifolds which are not Einstein. We also exhibit Jacobi-Videv algebraic curvature tensors where the Ricci operator defines an almost complex structure.