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Ricci decomposition
About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.
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TL;DR: In this article, a system of partial differential equations, whose solutions permit to determine explicitly locally homogeneous Lorentzian metrics in R3 having the prescribed admissible Ricci tensor, is introduced.
Abstract: We introduce a system of partial differential equations, whose solutions permit to determine explicitly locally homogeneous Lorentzian metrics in R3 having the prescribed admissible Ricci tensor. Solutions of this system are presented for all the different models of homogeneous Lorentzian three spaces.
10 citations
TL;DR: In this paper, the first eigenvalue of Dirac operator on a compact Riemannian spin manifold was proved by refined Weitzenbock techniques and applied to manifolds with harmonic curvature tensor.
Abstract: We prove a new lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold by refined Weitzenbock techniques. It applies to manifolds with harmonic curvature tensor and depends on the Ricci tensor. Examples show how it behaves compared to other known bounds.
9 citations
TL;DR: In this paper, it was shown that any four-dimensional Walker metric of nowhere zero scalar curvature has a natural almost para-Hermitian structure, and that if this structure is self-dual and *-Einstein, it is symplectic but not necessarily integrable.
Abstract: It is shown that any four-dimensional Walker metric of nowhere zero scalar curvature has a natural almost para-Hermitian structure. In contrast to the Goldberg–Sachs theorem, if this structure is self-dual and *-Einstein, it is symplectic but not necessarily integrable. This is due to the non-diagonalizability of the self-dual Weyl conformal curvature tensor.
9 citations
9 citations
TL;DR: In this paper, the Ricci curvature is defined as a measure for singular torsion-free connections on the tangent bundle of a manifold using an integral formula and vector-valued half-densities.
Abstract: We define the Ricci curvature, as a measure, for certain singular torsion-free connections on the tangent bundle of a manifold. The definition uses an integral formula and vector-valued half-densities. We give relevant examples in which the Ricci measure can be computed. In the time dependent setting, we give a weak notion of a Ricci flow solution on a manifold.
9 citations