English

A variational characterization of flat spaces in dimension three

Differential Geometry 2016-03-30 v1

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 σ2\sigma_{2}-curvature functional.

Keywords

Cite

@article{arxiv.1406.0990,
  title  = {A variational characterization of flat spaces in dimension three},
  author = {Giovanni Catino and Paolo Mastrolia and Dario D. Monticelli},
  journal= {arXiv preprint arXiv:1406.0990},
  year   = {2016}
}
R2 v1 2026-06-22T04:30:18.758Z