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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, it was shown that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected, using Hamilton Ricci ow with surgery, conformal method, and connected sum construction of Gromov and Lawson.
Abstract: In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected. The proof uses the Ricci ow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton’s Ricci ow is fundamental. As one of the applications we prove the path-connectedness of the space of trace-free asymptotically at solutions to the vacuum Einstein constraint equations on R 3 .
82 citations
TL;DR: In this paper, the authors study the space of regular Kahler metrics Eω, i.e. those for which deformation quantization has been defined by Cahen, Gutt and Rawnsley.
Abstract: Building on Donaldson’s work on constant scalar curvature metrics, we study the space of regular Kahler metrics Eω, i.e. those for which deformation quantization has been defined by Cahen, Gutt and Rawnsley. After giving, in Sects. 2 and 3 a review of Donaldson’s moment map approach, we study the ‘‘essential’’ uniqueness of balanced basis (i.e. of coherent states) in a more general setting (Theorem 2.5). We then study the space Eω in Sect.4 and we show in Sect.5 how all the tools needed can be defined also in the case of non-compact manifolds.
82 citations
TL;DR: In this article, the authors determine the topology of three-dimensional complete orientable Riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small.
Abstract: In this paper we determine the topology of three-dimensional complete orientable Riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small.
82 citations
TL;DR: In this paper, a scalar field is non-minimally coupled to both the torsion and a boundary term given by the divergence of the Torsion vector, and a dynamical crossing of the phantom barrier is also shown to be possible.
Abstract: We propose a new model in the teleparallel framework where we consider a scalar field nonminimally coupled to both the torsion $T$ and a boundary term given by the divergence of the torsion vector $B=\frac{2}{e}\partial_\mu (eT^\mu)$. This is inspired by the relation $R=-T+B$ between the Ricci scalar of general relativity and the torsion of teleparallel gravity. This theory in suitable limits incorporates both the nonminimal coupling of a scalar field to torsion, and the nonminimal coupling of a scalar field to the Ricci scalar. We analyse the cosmology of such models, and we perform a dynamical systems analysis on the case when we have only a pure coupling to the boundary term. It is found that the system generically evolves to a late time accelerating attractor solution without requiring any fine tuning of the parameters. A dynamical crossing of the phantom barrier is also shown to be possible.
82 citations
TL;DR: In this article, the authors derived sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant.
Abstract: We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4-manifold minimizes volume among all metrics satisfying a point-wise lower bound on sectional curvature plus suitable multiples of the scalar curvature. These estimates also imply new non-existence results for Einstein metrics.
81 citations