International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 4, Pages 161-193

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

Copyright © 2004 Bernd Ammann et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.