Topic
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: It is proved that if there exists a second order symmetric parallel tensor on a paracontact metric (k, µ)-space M, then either M is locally isometric to a product of a flat n + 1-dimensional manifold and an n-dimensional manifolds of constant sectional curvature −4, or the second order parallel Tensor is a constant multiple of the associated metric tensor g of M2n+1.
Abstract: The object of the present paper is to study the symmetric and skew-symmetric properties of a second order parallel tensor on paracontact metric (k, µ)-spaces and almost β-para-Kenmotsu (k, µ)-spaces. In this paper, we prove that if there exists a second order symmetric parallel tensor on a paracontact metric (k, µ)-space M, then either M is locally isometric to a product of a flat n + 1-dimensional manifold and an n-dimensional manifold of constant sectional curvature −4, or the second order parallel tensor is a constant multiple of the associated metric tensor g of M2n+1. If there is a second order parallel tensor on an almost β-para-Kenmotsu (k, µ)-space with k ≠ 0, then it is a constant multiple of the associated metric tensor g of M2n+1.
10 citations
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TL;DR: In this paper, it was shown that every Kaehler algebraic curvature tensor is geometrically realizable by a kaehler manifold of constant scalar curvature.
Abstract: We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a para-Kaehler manifold of constant scalar curvature
10 citations
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TL;DR: Crasmareanu et al. as mentioned in this paper obtained a 1-parameter family of Ricci solitons on a tangent bundle endowed with a pseudo-Riemannian metric of complete lift type.
10 citations
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TL;DR: In this paper, a local classification of all three-dimensional Riemannian manifolds whose Ricci tensor satisfies the equation ▿(ric-1 4 sg) = 1 20 ds ⊙ g is given.
Abstract: One derives a local classification of all three-dimensional Riemannian manifolds whose Ricci tensor satisfies the equation ▿(ric– 1 4 sg) = 1 20 ds ⊙ g.
10 citations
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TL;DR: The necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium) is that the Weyl tensor changes with respect to its value in the state-of-feasibility.
Abstract: It is shown that (except for two well defined cases), the necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium), is that the Weyl tensor changes with respect to its value in the state of equilibrium (or quasi-equilibrium).
10 citations