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, Chen-Yokota's argument was used to obtain a local lower bound of the scalar curvature for Ricci flow on complete manifolds. And if the curvature attains its minimum value at some point, then the manifold is Einstein.
Abstract: In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct (elliptic) proof of this sharp estimate. Moreover, if the scalar curvature attains its minimum value at some point, then the manifold is Einstein.
38 citations
TL;DR: In this article, a compact contact Ricci soliton with a potential vector field V collinear with the Reeb vector field, is shown to be the equivalent of an Eigenvector.
Abstract: We show that a compact contact Ricci soliton with a potential vector field V collinear with the Reeb vector field, is Einstein. We also show that a homogeneous H-contact gradient Ricci soliton is locally isometric to En+1 × Sn(4). Finally we obtain conditions so that the horizontal and tangential lifts of a vector field on the base manifold may be potential vector fields of a Ricci soliton on the unit tangent bundle.
38 citations
TL;DR: In this article, a space of tensors which transform covariantly under Weyl rescalings of the metric is built on a (pseudo-) Riemannian manifold of dimension n⩾3.
Abstract: On a (pseudo-) Riemannian manifold of dimension n⩾3, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl rescalings are also derived. These results are obtained by application of Becchi Rouet Stora Tyutin techniques.
38 citations
TL;DR: Information geometry of the Dicke model is studied, both with and without the rotating wave approximation, and it is shown that the parameter manifold is smooth even at the phase transition, and that the scalar curvature is continuous across the phase boundary.
Abstract: We study information geometry of the Dicke model, in the thermodynamic limit. The scalar curvature $R$ of the Riemannian metric tensor induced on the parameter space of the model is calculated. We analyze this both with and without the rotating wave approximation, and show that the parameter manifold is smooth even at the phase transition, and that the scalar curvature is continuous across the phase boundary.
38 citations
38 citations