Invariance of the Nayatani metrics for Kleinian manifolds

Katsuhiko Matsuzaki, Yasuhiro Yabuki

Research output: Contribution to journalArticle

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
Externally publishedYes

Fingerprint

Kleinian Groups
Invariance
Conformal Structure
Metric
Conformal Transformation
Isometry Group
Transformation group
Riemannian Metric
Divergence
Finite Group
Symmetry
Class
Standards

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Invariance of the Nayatani metrics for Kleinian manifolds. / Matsuzaki, Katsuhiko; Yabuki, Yasuhiro.

In: Geometriae Dedicata, Vol. 135, No. 1, 08.2008, p. 147-155.

Research output: Contribution to journalArticle

Matsuzaki, Katsuhiko ; Yabuki, Yasuhiro. / Invariance of the Nayatani metrics for Kleinian manifolds. In: Geometriae Dedicata. 2008 ; Vol. 135, No. 1. pp. 147-155.
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