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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, the authors consider the case when the immersed submanifold contains separable states or entangled states and show that a tensor field can encode some properties of these states.
Abstract: The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states Geometrical tensors are shown to encode some properties of these states These results are not unrelated with criteria already available in the literature We explicitly deal with some of these relations
16 citations
27 Sep 2006
TL;DR: In this article, the authors use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for tensors with the same symmetries as those of a torsion free, Ricci symmetric connection.
Abstract: We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally appear in relative hypersurface theory.
16 citations
TL;DR: In this article, a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs) is presented, considering cases when the Ricci tensor is both degenerate as well as non-degenerate.
Abstract: In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.
16 citations
TL;DR: Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U _h(su(1,1)) are considered in this paper.
Abstract: Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding Lie algebras.
16 citations
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TL;DR: In this paper, the Eisenhart problem of finding parallel tensors for the symmetric case in the regular $f$-Kenmotsu framework was solved for the Ricci tensors.
Abstract: The Eisenhart problem of finding parallel tensors is solved for the symmetric case in the regular $f$-Kenmotsu framework. On this way, the Olszack-Rosca example of Einstein manifolds provided by $f$-Kenmotsu manifolds via locally symmetric Ricci tensors is recovered as well as a case of Killing vector fields. Some other classes of Einstein-Kenmotsu manifolds are presented. Our result is interpreted in terms of Ricci solitons and special quadratic first integrals.
16 citations