Weakly Einstein critical metrics of the volume functional on compact manifolds with boundary

2018/04/27 by H. Baltazar, A. Da Silva, Baltazar, H. +3
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.1804.10706

openalex publication_date 2018/04/27 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to study weakly Einstein critical metrics of the volume functional on a compact manifold M with smooth boundary ∂ M. Here, we will give the complete classification for an n-dimensional, n=3 or 4, weakly Einstein critical metric of the volume functional with nonnegative scalar curvature. Moreover, in the higher dimensional case (n≥5), we will established a similar result for weakly Einstein critical metric under a suitable constraint on the Weyl tensor.

Citations

• Four dimensional static and related critical spaces with harmonic curvature
• Rigidity for critical metrics of the volume functional

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• Geometric inequalities for critical metrics of the volume functional
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