WebDefinition. Given a Riemannian metric g, the scalar curvature S (commonly also R, or Sc) is defined as the trace of the Ricci curvature tensor with respect to the metric: = . The scalar curvature cannot be computed directly from the Ricci curvature since the latter is a (0,2)-tensor field; the metric must be used to raise an index to obtain a (1,1)-tensor field … Web19 aug. 2015 · A well-known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature.
(PDF) Scalar curvature rigidity of certain symmetric spaces
Web23 dec. 2024 · [2012.12478] Waist inequality for 3-manifolds with positive scalar curvature We construct singular foliations of compact three-manifolds $(M^3,h)$ with scalar curvature $R_h\geq Λ_0>0$ by surfaces of controlled area, diameter This extends Urysohn and waist... Global Survey In just 3 minutes help us understand how you see … WebBased on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation principle for boundary conditions of metrics with lower scalar curvature bounds. This implies that … greg milligan country singer
Metric Inequalities with Scalar Curvature Semantic Scholar
WebWe establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. WebA Riemannian manifold endowed with k>2 orthogonal complementary distributions (called here an almost multi-product structure) appears in such topics as multiply twisted or warped products and the webs or nets composed of orthogonal foliations. In this article, we define the mixed scalar curvature of an almost multi-product structure endowed with a linear … WebPositive scalar curvature and exotic aspherical manifolds - Jialong DENG 邓嘉龙, YMSC Scalar curvature is interesting not only in analysis, geometry and topology but also in physics. For example, the positive mass theorem, which was proved by Schoen and Yau in 1979, is equivalent to the result that the three-dimension torus carries no Riemannian … greg minor mechanics