scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: In this article, it was shown that (M, g) is ℂℙ2 with its standard Fubini-Study metric, up to rescaling and isometry.
Abstract: Let (M, g) be a compact oriented four-dimensional Einstein manifold. If M has positive intersection form and g has non-negative sectional curvature, we show that, up to rescaling and isometry, (M, g) is ℂℙ2, with its standard Fubini–Study metric.

91 citations

Posted Content
TL;DR: In this paper, a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem are studied. But their focus is mainly on a conformal metric on a given Riemannian manifold.
Abstract: The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem.

91 citations

Journal ArticleDOI
Shin-ichi Ohta1
TL;DR: In this article, the existence of Euclidean tangent cones on Wasserstein spaces over compact Alexandrov spaces of curvature bounded below was established by using Riemannian structure.
Abstract: We establish the existence of Euclidean tangent cones on Wasserstein spaces over compact Alexandrov spaces of curvature bounded below. By using this Riemannian structure, we formulate and construct gradient flows of functions on such spaces. If the underlying space is a Riemannian manifold of nonnegative sectional curvature, then our gradient flow of the free energy produces a solution of the linear Fokker-Planck equation.

91 citations

Journal ArticleDOI
TL;DR: In this paper, the authors characterize the topology of 3D Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension.
Abstract: The purpose of this paper is to completely characterize the topology of three-dimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension.

91 citations


Network Information
Related Topics (5)
Moduli space
15.9K papers, 410.7K citations
92% related
Cohomology
21.5K papers, 389.8K citations
91% related
Abelian group
30.1K papers, 409.4K citations
88% related
Operator theory
18.2K papers, 441.4K citations
87% related
Invariant (mathematics)
48.4K papers, 861.9K citations
86% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023268
2022536
2021505
2020448
2019424
2018433