Energy and asymptotics of Ricci-flat 4-manifolds with a Killing field

Abstract

If a complete 4-manifold with Ric = 0 has a nowhere zero Killing field, we prove it is flat, generalizing a classic result on compact manifolds. If the Killing field has compact zero-locus, we compute the manifold's L 2 energy.Date: August 22, 2017.2010 Mathematics Subject Classification. 53C26, 53C24 (primary), and 58J60 (secondary).