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Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group

In: Rigidity in Dynamics and Geometry

Author

Listed:
  • Sa’ar Hersonsky

    (Ben Gurion University, Department of Mathematics)

  • Frédéric Paulin

    (UMR 8553 CNRS, École Normale Supérieure, Département de Mathématiques et Applications)

Abstract

This paper is a survey of the work of the authors [21], [2], [22], with a new application to Diophantine approximation in the Heisenberg group. The Heisenberg group, endowed with its Carnot-Carathéodory metric, can be seen as the space at infinity of the complex hyperbolic space (minus one point). The rational approximation on the Heisenberg group can be interpreted and developed using arithmetic subgroups of SU (n, 1). In the appendix, the case of hyperbolic surfaces is developed by Jouni Parkkonen and the second author.

Suggested Citation

  • Sa’ar Hersonsky & Frédéric Paulin, 2002. "Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group," Springer Books, in: Marc Burger & Alessandra Iozzi (ed.), Rigidity in Dynamics and Geometry, pages 203-226, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04743-9_10
    DOI: 10.1007/978-3-662-04743-9_10
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