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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 conformal Killing tensor of degree p in a Sasakian space is studied and a decomposition theorem is proved for the form of the associated tensor.
Abstract: We deal with a horizontal conformal Killing tensor of degree p in a Sasakian space. After some preparations we prove that a horizontal conformal Killing tensor of odd degree is necessarily Killing. Moreover, we consider horizontal conformal Killing tensor of even degree. The form of the associated tensor is determined completely and a decomposition theorem is proved. Then we give the examples of a conformal Killing tensor of even degree and a special Killing tensor of odd degree with constant l.
7 citations
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TL;DR: In this article, a formalism based on the description of a geometry in terms of the curvature tensor and its covariant derivatives is used to show that there are no tilted dust exact power law (EPL) cosmologies.
Abstract: A formalism based on the description of a geometry in terms of the curvature tensor and its covariant derivatives is used to show that there are no tilted dust exact power law (EPL) cosmologies.
7 citations
TL;DR: In this paper, the authors define the tensor differential operators: divergence, curl and gradient, which act on a tensor of any rank, in terms of C-G coefficients, and obtain a matrix representation and useful properties for those operators.
Abstract: The quantum theory of angular momentum affords a treatment of tensors and vectors in a spherical basis. By using this theory we define the tensor differential operators: divergence, curl and gradient which act on a tensor of any rank, in terms of C-G coefficients. With these definitions we obtain a matrix representation and useful properties for those operators. An interesting application of this formalism is to find the wave equation of a tensor of any rank in a linear theory. This provides a new common way to look at the wave equations associated with both Maxwell's equations and the Maxwell-like equations for the linearized Weyl curvature tensor in gravitoelectromagnetism describing gravitational radiation on a Minkowski spacetime background.
7 citations
01 Oct 1988
TL;DR: In this article, the authors estimate the order of the isometry groups of compact manifolds with negative Ricci curvature in terms of geometric quantities: the sectional curvature, the Ricci curve, the diameter, and the injectivity radius.
Abstract: We estimate the order of the isometry groups of compact manifolds with negative Ricci curvature in terms of geometric quantities: the sectional curvature, the Ricci curvature, the diameter, and the injectivity radius.
7 citations
Book•
24 Mar 2016
TL;DR: This paper presents a probabilistic procedure for estimating the rank of the determinantal polynomials of the Tensor Rank using three different types of Tensors: Nonsingular, Determinantal and Determinants.
Abstract: Basics of Tensor Rank.- 3-Tensors.- Simple Evaluation Methods of Tensor Rank.- Absolutely Nonsingular Tensors and Determinantal Polynomials.- Maximal Ranks.- Typical Ranks.- Global Theory of Tensor Ranks.- 2 x 2 x * * * x 2 Tensors.
6 citations