2009/10/30 by Vincent Minerbe, Minerbe, Vincent · 1 citation
Mathematics · Physics and Astronomy · #53C20 #53C24 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C20 #msc:53C24
paper · pdf · doi:10.48550/arxiv.0910.5792
arxiv created 2009/10/30 · arxiv updated 2009/12/01
This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperkähler manifold asymptotic to a circle fibration over the Euclidean three-space is either the standard \rl3 × \sph1 or a multi-Taub-NUT manifold. In particular, the underlying complex manifold is either \cx × \cx/\ir or a minimal resolution of a cyclic Kleinian singularity.