Diophantine Approximation in Negatively Curved Manifolds and in the Heisenberg Group

Sa’ar Hersonsky () and Frédéric Paulin ()
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Sa’ar Hersonsky: Ben Gurion University, Department of Mathematics
Frédéric Paulin: UMR 8553 CNRS, École Normale Supérieure, Département de Mathématiques et Applications

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 203-226 from Springer

Abstract: 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.

Keywords: Critical Exponent; Heisenberg Group; Constant Curvature; Hausdorff Dimension; Discrete Subgroup (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_10

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DOI: 10.1007/978-3-662-04743-9_10

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