International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 4, Pages 161-193
doi:10.1155/S0161171204212108

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

Bernd Ammann,1 Robert Lauter,2 and Victor Nistor3

 1Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, Hamburg D-20146, Germany
2Fachbereich Mathematik, Universität Mainz, Mainz D-55099, Germany
3Department of Mathematics, Pennsylvania State University, University Park, 16802, PA, USA
Received 16 December 2002

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.