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Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group

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Rigidity in Dynamics and Geometry

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University, Beer-Sheva, Israel

    Sa’ar Hersonsky

  2. Département de Mathématiques et Applications, UMR 8553 CNRS, École Normale Supérieure, 45 rue d’Ulm, 75230, PARIS Cedex 05, France

    Frédéric Paulin

Authors
  1. Sa’ar Hersonsky
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  2. Frédéric Paulin
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Editor information

Editors and Affiliations

  1. Forschungsinstitut für Mathematik, ETH Zentrum, Rämistraße 101, 8092, Zürich, Schweiz

    Marc Burger  & Alessandra Iozzi  & 

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Hersonsky, S., Paulin, F. (2002). Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group. In: Burger, M., Iozzi, A. (eds) Rigidity in Dynamics and Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04743-9_10

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  • DOI: https://doi.org/10.1007/978-3-662-04743-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07751-7

  • Online ISBN: 978-3-662-04743-9

  • eBook Packages: Springer Book Archive

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