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, the authors investigated various cases in which the value zero is attained and showed that it occurs in some situations where space-time is of an algebraically special type.
Abstract: The Bel–Robinson tensor is a rank 4 tensor constructed from the Weyl curvature tensor. It is well known that when it is contracted with four future-pointing vectors a non-negative value is always obtained. In this paper we investigate various cases in which the value zero is attained and show that it occurs in some situations where space–time is of an algebraically special type. This is of importance for expressions of gravitational energy related to the Bel–Robinson tensor. Some new invariant ways of classifying the Petrov type of space–times using the Bel–Robinson tensor are also presented.
37 citations
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TL;DR: In this article, it was shown that any Weyl curvature model can be geometrically realized by a Weyl manifold, and that the manifold can be used to represent the Weyl curve.
37 citations
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TL;DR: In this article, a set of necessary and sufficient conditions for an ann-dimensional semi-Riemannian manifold to be conformal to an Einsteinspace is presented.
Abstract: This paper presents a set of necessary and sufficient conditions for ann-dimensional semi-Riemannian manifold to be conformal to an Einstein space We extend results due to C N Kozameh, E T Newman and K P Tod who solved the problem in the four-dimensional Lorentz case formanifolds with nondegenerate Weyl tensor, ie for spacetimes withJ ≠ 0 In particular, in n-dimension we will find tensorialconditions if the Weyl tensor operates injectively on the alternatingtwo-forms Moreover, in the four-dimensional Riemannian case we canalways decide whether a manifold is locally conformal to an Einsteinspace
37 citations
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TL;DR: In this paper, the Bakry-Emery Ricci curvature tensor is used to prove the Myers compactness theorem for complete and connected Riemannian manifold of dimension n.
Abstract: Let (M, g) be a complete and connected Riemannian manifold of dimension n. By using the Bakry–Emery Ricci curvature tensor on M, we prove two theorems which correspond to the Myers compactness theorem.
37 citations
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TL;DR: In this paper, the authors studied the problem of finding complete conformal metrics determined by a symmetric function of Ricci tensors in a negative convex cone on compact manifolds, and showed that any smooth bounded domain in Euclidean space of dimension greater or equal to 3 admits a complete conformally flat metric of negative Ricci curvature with.
Abstract: We study the problem of finding complete conformal metrics determined by a symmetric function of Ricci tensor in a negative convex cone on compact manifolds. A consequence of our main results is that any smooth bounded domain in Euclidean space of dimension greater or equal to 3 admits a complete conformally flat metric of negative Ricci curvature with .
37 citations