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arXiv · 1703.01819

Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary

H. Baltazar·E. Ribeiro Jr
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Abstract

We provide a general B\"ochner type formula which enables us to prove some rigidity results for $V$-static spaces. In particular, we show that an $n$-dimensional positive static triple with connected boundary and positive scalar curvature must be isometric to the standard hemisphere, provided that the metric has zero radial Weyl curvature and satisfies a suitable pinching condition. Moreover, we classify $V$-static spaces with non-negative sectional curvature.

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H. Baltazar, E. Ribeiro Jr. 2017-03-06. Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary. https://doi.org/10.2140/pjm.2018.297.29

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