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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 local classification of pseudo-Riemannian manifolds with parallel Weyl tensors that are not conformally flat or locally symmetric has been presented.
Abstract: This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.
12 citations
TL;DR: In this article, the connection between the critical point structure of the Riemannian curvature function and the Petrov classification of the Ricci tensor has been investigated, and a similar function is defined whose critical point structures are connected with the algebraic classification of RicCI tensors.
Abstract: Some theorems proved by Thorpe concerning the connection between the critical point structure of the Riemannian (sectional) curvature function and the Petrov classification are extended. A similar function is defined whose critical point structure is connected with the algebraic classification of the Ricci tensor.
12 citations
04 Oct 2000
TL;DR: In this article, the problem of finding metrics j conformal to the pseudo-Euclidean metric g such that Ric g = T was studied and the solution was obtained by the diagonal elements.
Abstract: We consider constant symmetric tensors T on R', n > 3, and we study the problem of finding metrics j conformal to the pseudo-Euclidean metric g such that Ric g = T. We show that such tensors are determined by the diagonal elements and we obtain explicitly the metrics 9. As a consequence of these results we get solutions globally defined on Rn for the equation -So\g~So + njIVgsoI2/2 + AWo2 = 0. Moreover, we show that for certain unbounded functions K defined on Rn, there are metrics conformal to the pseudo-Euclidean metric with scalar curvature K.
12 citations
TL;DR: In this paper, the reduction of n-fold tensor products of induced unitary representations of noncompact groups into irreducible constituents is shown. And the coefficients of the Clebsch-Gordon coefficients are calculated.
Abstract: The reduction ofn-fold tensor products of induced unitary representations of noncompact groups into irreducible constituents is shown. Clebsch-Gordon coefficients are then calculated. The technique is applied to then-fold tensor products of the positive mass representations of the Poincare group.
12 citations
TL;DR: In this article, it was shown that every irreducible compact compact Kahler surface with δW − = 0 is a Kahler-Einstein surface and is biholomorphic to a ruled extremal kahler surface.
Abstract: We prove that every irreducible compact Kahler surface with δW − =0 is Kahler–Einstein or is biholomorphic to a ruled extremal Kahler surface.
12 citations