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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 paper, the transmission of Weyl's theorem from operators on Banach spaces to their tensor products, and also to their associated multiplication operators, is deconstructed, and the Weyl theorem is reconstructed.
Abstract: The transmission of “Weyl’s theorem” from operators on Banach spaces to their tensor products, and also to their associated multiplication operators, is deconstructed.
17 citations
TL;DR: The Ricci tensor is a natural weakening of the Einstein condition in almost Hermitian geometry as mentioned in this paper, which is a weaker version of the Ricci condition in Cartesian geometry.
Abstract: The J -invariance of the Ricci tensor is a natural weakening of the Einstein condition in almost Hermitian geometry. The aim of this paper is to determine left-invariant strictly almost Kahler structures ( g , J , Ω ) on real 4-dimensional Lie groups such that the Ricci tensor is J -invariant. We prove that all these Lie groups are isometric (up to homothety) to the (unique) 4-dimensional proper 3-symmetric space.
17 citations
TL;DR: In this paper, an algebraic method is presented to determine the components of the metric tensor up to an arbitrary conformal factor, from a given set of components of its Riemann tensor Rmu nu alpha beta in some coordinate frame.
Abstract: An algebraic method is presented, which shows how to determine the components of the metric tensor gmu nu , up to an arbitrary conformal factor, from a given set of components of its Riemann tensor Rmu nu alpha beta in some coordinate frame. This procedure follows and generalises one given by Ihrig (1975). Since the computations are purely algebraic and are carried out at a point in the manifold, no differentiability or continuity conditions are assumed. A number of examples are given to illustrate the technique. Although the method determines the metric up to one arbitrary scalar, in a number of cases either one or three other arbitrary scalars arise. These latter cases are rare, and the form of the Riemann tensor for such cases have been listed elsewhere.
17 citations
TL;DR: The algebra of irreducible tensor operators is developed in the intermediate-field coupling case in this article, and the Wigner-Eckart theorem is formulated for a simple irreducer tensor operator as well as for the Kronecker and scalar products of these operators.
Abstract: The algebra of irreducible tensor operators is developed in the intermediate-field coupling case. The Wigner-Eckart theorem is formulated for a simple irreducible tensor operator as well as for the Kronecker and scalar products of these operators. The expressions required for the calculation of Coulomb repulsion, crystal field splitting, spin-orbit interaction, and Zeeman effect are given in detail. Recent applications to various problems in spectroscopy and magnetism of transition metal compounds are referred to.
17 citations
TL;DR: In this article, a method of calculating the metric from the curvature of a tensor with the symmetry properties of a type D curvature tensor is given in an orthonormal tetrad.
Abstract: A method of calculating the metric from the curvature is presented. Assuming that a tensor with the symmetry properties of a type D curvature tensor is given in an orthonormal tetrad, we use the Bianchi identities and the relationship between the connection and the tetrad in order to calculate, under certain assumptions, the corresponding metric. Some well-known metrics are derived from the curvature by using the method given here.
17 citations