Topic
Scalar curvature
About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.
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TL;DR: In this article, the authors studied conformal vector fields on pseudo-Riemannian manifolds, in particular on Einstein spaces and on spaces of constant scalar curvature.
Abstract: We study conformal vector fields on pseudo-Riemannian manifolds, in particular on Einstein spaces and on spaces of constant scalar curvature. A global classification theorem for conformal vector fields is obtained which are locally gradient fields. This includes the case of a positive metric as well as the case of an indefinite metric.
73 citations
TL;DR: The scale space image of the distance accumulation showed that the zero crossings of distance accumulation are quite stable and analysis of its relation to planar curvature matched very well with experimental results.
73 citations
TL;DR: In this article, the curvature perturbation is defined in a gauge invariant manner with this ''dark matter'' taken into account, and conditions under which the curvatures are conserved on large scales.
Abstract: In the non-relativistic theory of gravity recently proposed by Horava, the Hamiltonian constraint is not satisfied locally at each point in space. The absence of the local Hamiltonian constraint allows the system to have an extra dark-matter-like component as an integration constant. We discuss consequences of this fact in the context of cosmological perturbations, paying a particular attention to the large scale evolution of the curvature perturbation. The curvature perturbation is defined in a gauge invariant manner with this ``dark matter'' taken into account. We then clarify the conditions under which the curvature perturbation is conserved on large scales. This is done by using the evolution equations.
73 citations
Book•
27 Nov 2013
TL;DR: The Dirichlet Problem of the CMC Equation in Unbounded Domains was studied in this paper, where the area and the volume of a Constant Mean Curvature Surface were derived.
Abstract: Introduction.- Surfaces with Constant Mean Curvature.- Constant Mean Curvature Embedded Surfaces.- The Flux Formula for Constant Mean Curvature Surfaces.- The Area and the Volume of a Constant Mean Curvature Surface.- Constant Mean Curvature Discs with Circular Boundary.- The Dirichlet Problem of the CMC Equation.- The Dirichlet Problem in Unbounded Domains.- Constant Mean Curvature Surfaces in Hyperbolic Space.- The Dirichlet Problem in Hyperbolic Space.- Constant Mean Curvature Surfaces in Lorentz-Minkowski Space.- Appendix: A. The Variation Formula of the Area and the Volume.- B. Open Questions.- References.
73 citations
TL;DR: In this paper, the trace of the energy-momentum tensor in terms of normal products is defined and the results of Tseytlin and also of Curci and Paffuti recovered.
73 citations