Invariance of the Nayatani metrics for Kleinian manifolds

Katsuhiko Matsuzaki; Yasuhiro Yabuki

doi:10.1007/s10711-008-9268-7

Invariance of the Nayatani metrics for Kleinian manifolds

Katsuhiko Matsuzaki, Yasuhiro Yabuki^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	147-155
Number of pages	9
Journal	Geometriae Dedicata
Volume	135
Issue number	1
DOIs	https://doi.org/10.1007/s10711-008-9268-7
Publication status	Published - 2008 Aug
Externally published	Yes

Keywords

Divergence type
Kleinian group
Nayatani metric
Patterson-Sullivan measure

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-008-9268-7

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AB - 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.

KW - Divergence type

KW - Kleinian group

KW - Nayatani metric

KW - Patterson-Sullivan measure

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Invariance of the Nayatani metrics for Kleinian manifolds

Abstract

Keywords

ASJC Scopus subject areas

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