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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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01 Jan 2004
TL;DR: In this paper, the authors give an algebraic classification of space-times satisfying some pseudo-symmetric type conditions based on the classification of the Weyl and Ricci tensors.
Abstract: We give an algebraic classification of space-times satisfying some pseudo- symmetry type conditions based on the classification of the Weyl and Ricci tensor. It is shown that for non-conformally flat space-times pseudo-symmetry and Weyl- pseudo-symmetry are equivalent. We show further that the only space-times that have a pseudo-symmetric Weyl tensor are of Petrov type D.
18 citations
TL;DR: In this paper, it was shown that a complete non-compact manifold with nonnegative Ricci curvature has a trivial codimension one homology unless it is a flat normal bundle over a compact totally geodesic submanifold.
Abstract: In this paper we prove that a complete noncompact manifold with nonnegative Ricci curvature has a trivial codimension one homology unless it is a flat normal bundle over a compact totally geodesic submanifold. In particular, we prove the conjecture that a complete noncompact manifold with positive Ricci curvature has a trivial codimension one integer homology. We also have a corollary stating when the codimension two integer homology of such a manifold is torsion free.
18 citations
TL;DR: In this article, it was shown that there is a 2-invariant Riemannian metric of positive Ricci curvature on every 4-dimensional simply connected T 2-manifold.
Abstract: We prove that there is a T
2-invariant Riemannian metric of positive Ricci curvature on every four-dimensional simply connected T
2-manifold.
17 citations
TL;DR: An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given in this article.
Abstract: An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained.
17 citations
01 Mar 2012
TL;DR: Ghosh et al. as mentioned in this paper studied Ricci solitons on a Riemannian manifold whose metric is a Ricci tensor and showed that Ricci is a generalization of the Einstein metric and is defined on the manifold by ( £ V g) + 2 S(X,Y) +2 R ij projected from the space of metrics onto its quotient modulodiffeomorphisms and scalings.
Abstract: We study η -Einstein K -contact manifold whose metric is a Ricci soliton. Keywords Ricci soliton · K -contact metric · η -Einstein Mathematics Subject Classification (2000) 53C25 · 53C44 ·53C21 1 Introduction A Riemannian metric g on a smooth manifold is Einstein if its Ricci tensor S is aconstant multiple of g . A Ricci soliton is a generalization of the Einstein metric andis defined on a Riemannian manifold ( M,g )by ( £ V g)(X,Y) +2 S(X,Y) +2 λg(X,Y) = 0(1)for some constant λ , a vector field V , and arbitrary vector fields X,Y on M .TheRicci soliton is said to be shrinking, steady, and expanding according as λ is negative,zero, and positive respectively. Compact Ricci solitons are the fixed points of the Ricciflow: ∂∂t g ij =−2 R ij projected from the space of metrics onto its quotient modulodiffeomorphisms and scalings, and often arise as blow-up limits for the Ricci flow on A. Ghosh ( B )Department of Mathematics, Krishnagar Government College,Krishnanagar, West Bengal, 741101, Indiae-mail: aghosh_70@yahoo.comR. SharmaDepartment of Mathematics, University of New Haven,West Haven, CT 06516, USAe-mail: rsharma@newhaven.edu
17 citations