We prove that, in dimension three, flat metrics are the only complete metrics with nonnegative scalar curvature which are critical for the σ2-curvature functional.
A variational characterization of flat spaces in dimension three / G. Catino, P. Mastrolia, D.D. Monticelli. - In: PACIFIC JOURNAL OF MATHEMATICS. - ISSN 0030-8730. - 282:2(2016), pp. 285-292.
A variational characterization of flat spaces in dimension three
P. MastroliaSecondo
;
2016
Abstract
We prove that, in dimension three, flat metrics are the only complete metrics with nonnegative scalar curvature which are critical for the σ2-curvature functional.
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