A variational characterization of flat spaces in dimension three

Giovanni Catino, Paolo Mastrolia and Dario D. Monticelli

Vol. 282 (2016), No. 2, 285–292

DOI: 10.2140/pjm.2016.282.285

Abstract

We prove that, in dimension three, flat metrics are the only complete metrics with nonnegative scalar curvature which are critical for the ${\sigma }_2$-curvature functional.

Keywords

critical metrics, quadratic functionals, rigidity results

Mathematical Subject Classification 2010

Primary: 53C24

Secondary: 53C25

Milestones

Received: 15 March 2015

Accepted: 19 July 2015

Published: 3 March 2016