Minerbe, Vincent On the asymptotic geometry of gravitational instantons. (English) Zbl 1215.53043 Ann. Sci. Éc. Norm. Supér. (4) 43, No. 6, 883-924 (2010). The author investigates the geometry at infinity of gravitational instantons, or asymptotically flat hyper-Kähler four-manifolds. His main result states that gravitational instantons with cubic volume growth are asymptotically locally flat, that is, asymptotic to a circle fibration over a Euclidean space of dimension three, with fibers of asymptotically constant length. In Appendix A, the author sharpens his result from [Geom. Funct. Anal. 18, No. 5, 1696–1749 (2008; Zbl 1166.53028)] on the bound of the derivatives of the curvature of a Ricci flat manifold. Reviewer: Witold Mozgawa (Lublin) Cited in 18 Documents MSC: 53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry 53C80 Applications of global differential geometry to the sciences 53C29 Issues of holonomy in differential geometry Keywords:gravitational instantons; hyper-Kähler manifolds; asymptotically locally flat manifolds; asymptotically locally Euclidean; injectivity radius; volume growth; Taub-NUT metric; fundamental pseudo-group; holonomy; local fibration Citations:Zbl 1166.53028 PDFBibTeX XMLCite \textit{V. Minerbe}, Ann. Sci. Éc. Norm. Supér. (4) 43, No. 6, 883--924 (2010; Zbl 1215.53043) Full Text: DOI Link