Deformations of hyperbolic 3-cone-manifolds

Research output: Contribution to journalArticle

46 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 languageEnglish
Pages (from-to)469-516
Number of pages48
JournalJournal of Differential Geometry
Volume49
Issue number3
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

Fingerprint

Cone
Rigidity
Angle
Hyperbolic Manifold
Homeomorphic
Complement
Singularity
Imply

Keywords

  • Cone-manifold
  • Deformation
  • Hyperbolic manifold
  • Rigidity

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Deformations of hyperbolic 3-cone-manifolds. / Kojima, Sadayoshi.

In: Journal of Differential Geometry, Vol. 49, No. 3, 01.01.1998, p. 469-516.

Research output: Contribution to journalArticle

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