Topic
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, it was shown that compact pseudo-Riemannian manifold with parallel Weyl tensor without being conformally flat or locally symmetric can be found in infinitely many dimensions greater than 4.
26 citations
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TL;DR: In this paper, the Ricci tensor of a (semi-)Riemannian manifold (M,g) and its Ricci Tachibana tensor ∧g⋅S, where the natural metrical operator ∧ g also acts as a derivation on S, is studied.
26 citations
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TL;DR: In this article, the authors present representations of Hecke and in non-describing characteristics for Mathematics Subject Classification: 20C20, 20C33, 20G05 and 20G40.
Abstract: Representations of Hecke and in non-describing characteristics. 1991 Mathematics Subject Classification: 20C20, 20C33, 20G05, 20G40.
26 citations
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Abstract: The Eisenhart problem of finding parallel and symmetric tensors is considered in the framework ofN (k)-quasi Einstein manifolds and the result is connected with Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is: i) shrinking on a class of conformally flat perfect fluid space-times and on quasi-umbilical hypersurfaces, in particular unit spheres; ii) expanding if the generator is of torse-forming type.
26 citations
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TL;DR: In this paper, the Ricci tensor and conformal Killing fields are used to define the center of mass of an asymptotically flat manifold and their alternative definitions depending on Ricci's tensor tensor.
Abstract: We prove in a simple and coordinate-free way the equivalence bteween the classical definitions of the mass or the center of mass of an asymptotically flat manifold and their alternative definitions depending on the Ricci tensor and conformal Killing fields. This enables us to prove an analogous statement in the asymptotically hyperbolic case.
25 citations