Einstein and scalar flat Riemannian metrics

2019/11/07 by Santiago R. Simanca, Simanca, Santiago R
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1911.02706

openalex publication_date 2019/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On a given closed connected manifold of dimension two, or greater, we consider the squared L²-norm of the scalar curvature functional over the space of constant volume Riemannian metrics. We prove that its critical points have constant scalar curvature, and use this to show that a metric is a solution of the critical point equation if, and only if, it is either Einstein, or scalar flat.

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