vix.ing · top · new · best · stats · spec

Scalar curvature under the collapse of metric

2022/10/28 by Khoi Nguyen, Nguyen, Khoi
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.2210.16163

Abstract

We prove a formula involving the scalar curvature of a Riemannian manifold endowed with a distribution in terms of an adapted orthonormal frame for its tangent bundle. Using the formula, we then investigate the effect of collapsing the metric along the distribution on the scalar curvature. This result contributes to the question of finding a positive scalar curvature metric on a Riemannian manifold.

Related