Deformations of hyperbolic 3-cone-manifolds

Sadayoshi Kojima

doi:10.4310/jdg/1214461108

Deformations of hyperbolic 3-cone-manifolds

Sadayoshi Kojima^*

^*Corresponding author for this work

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

49 Citations (Scopus)

Abstract

We show that any compact orientable hyperbolic 3-cone-manifold with cone angles at most π can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local rigidity by Hodgson and Kerckhoff implies the global rigidity for compact orientable hyperbolic 3-cone-manifolds under the same angle assumption.

Original language	English
Pages (from-to)	469-516
Number of pages	48
Journal	Journal of Differential Geometry
Volume	49
Issue number	3
DOIs	https://doi.org/10.4310/jdg/1214461108
Publication status	Published - 1998
Externally published	Yes

Keywords

Cone-manifold
Deformation
Hyperbolic manifold
Rigidity

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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10.4310/jdg/1214461108

Cite this

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title = "Deformations of hyperbolic 3-cone-manifolds",

abstract = "We show that any compact orientable hyperbolic 3-cone-manifold with cone angles at most π can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local rigidity by Hodgson and Kerckhoff implies the global rigidity for compact orientable hyperbolic 3-cone-manifolds under the same angle assumption.",

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AB - We show that any compact orientable hyperbolic 3-cone-manifold with cone angles at most π can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local rigidity by Hodgson and Kerckhoff implies the global rigidity for compact orientable hyperbolic 3-cone-manifolds under the same angle assumption.

KW - Cone-manifold

KW - Deformation

KW - Hyperbolic manifold

KW - Rigidity

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JF - Journal of Differential Geometry

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ER -

Deformations of hyperbolic 3-cone-manifolds

Abstract

Keywords

ASJC Scopus subject areas

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