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: In this article, conformal vector fields on space-times which are compatible with the Ricci tensor (so-called conformal Ricci collineations) are studied.
Abstract: We study conformal vector fields on space-times which in addition are compatible with the Ricci tensor (so-called conformal Ricci collineations). In the case of Einstein metrics any conformal vector field is automatically a Ricci collineation as well. For Riemannian manifolds, conformal Ricci collineation were called concircular vector fields and studied in the relationship with the geometry of geodesic circles. Here we obtain a partial classification of space-times carrying proper conformal Ricci collineations. There are examples which are not Einstein metrics.
19 citations
TL;DR: In this paper, Manvelyan and Ruhl presented the analysis of the linearized trace anomaly obtained from the quadratic part of the effective action for a conformally coupled scalar with linearized interaction with the external higher spin fields.
19 citations
TL;DR: A symplectic time-discretization splitting scheme that preserves the Hamiltonian properties of the Vlasov–Poisson system is suggested, naturally obtained by considering the tensor structure of the approximation.
19 citations
TL;DR: In this paper, the authors classify 4-dimensional Einstein-like manifolds whose Ricci tensor has constant eigenvalues (this being a special kind of curvature homogeneity condition).
Abstract: The aim of this paper is to classify 4-dimensional Einstein-like manifolds whose Ricci tensor has constant eigenvalues (this being a special kind of curvature homogeneity condition). We give a full classification when the Ricci tensor is of Codazzi type; when the Ricci tensor is cyclic parallel, we classify all such manifolds when not all Ricci curvatures are distinct. In this second case we find a one-parameter family of Riemannian metrics on a Lie groupG as the only possible ones which are irreducible and non-symmetric.
19 citations
TL;DR: In this paper, a unified framework for a Weitzenböck formula for a large class of canonical metrics on four-manifolds was established, including Kähler-Einstein metrics and Hermitian, Einstein metrics with positive scalar curvatures.
Abstract: We first provide an alternative proof of the classical Weitzenböck formula for Einstein four-manifolds using Berger curvature decomposition, motivated by which we establish a unified framework for a Weitzenböck formula for a large class of canonical metrics on four-manifolds. As applications, we classify Einstein four-manifolds and conformally Einstein four-manifolds with half two-nonnegative curvature operator, which in some sense provides a characterization of Kähler-Einstein metrics and Hermitian, Einstein metrics with positive scalar curvature on four-manifolds, respectively. We also discuss the classification of four-dimensional gradient shrinking Ricci solitons with half two-nonnegative curvature operator and half harmonic Weyl curvature.
19 citations