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

Author

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  • Bernd Ammann
  • Robert Lauter
  • Victor Nistor

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.

Suggested Citation

  • Bernd Ammann & Robert Lauter & Victor Nistor, 2004. "On the geometry of Riemannian manifolds with a Lie structure at infinity," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-33, January.
    • Handle: RePEc:hin:jijmms:484912
    DOI: 10.1155/S0161171204212108
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    Cited by:

    1. Olesya Grishchenko & Xiao Han & Victor Nistor, 2018. "A volatility-of-volatility expansion of the option prices in the SABR stochastic volatility model," Papers 1812.09904, arXiv.org.

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