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arXiv · 1406.0990

A variational characterization of flat spaces in dimension three

Giovanni Catino·Paolo Mastrolia·Dario D. Monticelli
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Abstract

In this short note we prove that, in dimension three, flat metrics are the only complete metrics with non-negative scalar curvature which are critical for the $\sigma_{2}$-curvature functional.

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Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli. 2014-06-04. A variational characterization of flat spaces in dimension three. https://doi.org/10.2140/pjm.2016.282.285

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