On the geometry of Riemannian manifolds with a Lie structure at infinity

2002/01/31 by Bernd Ammann, Robert Lauter, Victor Nistor · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #math.AP #math.DG #math.SP

paper · pdf · doi:10.1155/s0161171204212108

published as Int. J. Math. and Math. Sciences 2004:4 (2004) 161--193 · LaTeX

arxiv created 2003/08/29 · openalex publication_date 2004/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study a generalization of the geodesic spray and give conditions for noncomapct manifolds with a Lie structure at infinity to have positive injectivity radius. We also prove that the geometric operators are generated by the given Lie algebra of vector fields. This is the first one in a series of papers devoted to the study of the analysis of geometric differential operators on manifolds with Lie structure at infinity.

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• Singular spaces, groupoids and metrics of positive scalar curvature
• Uniform Shapiro-Lopatinski Conditions and Boundary Value Problems on Manifolds with Bounded Geometry