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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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7 citations
01 Jan 1977
TL;DR: In this paper, the authors first proved the reduction of codimension of minima-1 immersions to a (n+l)-dimensiona1 space of constant curvature.
Abstract: In this paper we first prove the fo11owing theorem on reduction of codimension of minima1 immersions: Theorem 1 - Let x: Mn→X be a minima1 immersion of an n-dimensiona1 connected manifold Mn into an (n+l)-dimensiona1 space X of constant curvature. Assume that the curvature tensor of the norma1 connexion is paral1e1 in the norma1 bundle and the first norma1 space of the immersion has constant dimension k.
7 citations
TL;DR: In this paper, it was shown that the symmetrized product of K-compatible tensors is a special Jordan algebra, i.e., the symmetric product of k-compatible symmetric tensors form a special algebra.
Abstract: Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor $b_{ij}$ is named `compatible' with the curvature tensor if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} + b_k{}^m K_{ijlm} = 0$. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetrized product of K-compatible tensors is K-compatible.
7 citations
TL;DR: In this paper, necessary and sufficient conditions are given on a constant symmetric tensor Tij on Rn, n≥3, for which there exist metrics ḡ, conformal to a pseudo-Euclidean metric g, such that Rij−12Kgij=Tij, where Rij and K are the Ricci tensor and the scalar curvature of
7 citations
TL;DR: In this paper, it was shown that every irreducible compact Kahler manifold with harmonic Bochner curvature tensor and negative semi-definite Ricci tensor is a Kahler-Einstein manifold.
Abstract: We prove that every irreducible Kahler manifold with harmonic Bochner curvature tensor and constant scalar curvature is Kahler–Einstein and that every irreducible compact Kahler manifold with harmonic Bochner curvature tensor and negative semi-definite Ricci tensor is Kahler–Einstein.
7 citations