Invariance of the Nayatani metrics for Kleinian manifolds

Katsuhiko Matsuzaki, Yasuhiro Yabuki

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2 Citations (Scopus)

Abstract

The Nayatani metric g N is a Riemannian metric on a Kleinian manifold M which is compatible with the standard flat conformal structure. It is known that, for M corresponding to a geometrically finite Kleinian group, g N has large symmetry: the isometry group of (M, g N ) coincides with the conformal transformation group of M. In this paper, we prove that this holds for a larger class of M. In particular, this class contains such M that correspond to Kleinian groups of divergence type.

Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalGeometriae Dedicata
Volume135
Issue number1
DOIs
Publication statusPublished - 2008 Aug 1

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Keywords

  • Divergence type
  • Kleinian group
  • Nayatani metric
  • Patterson-Sullivan measure

ASJC Scopus subject areas

  • Geometry and Topology

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