A characterization of spherical polyhedral surfaces

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Abstract

A spherical polyhedral surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedral surface. This paper investigates these surfaces from the point of view of inner angles. A rigidity result is obtained. A characterization of spherical polyhedral surfaces in terms of the triangulation and the angle assignment is established.

Original languageEnglish (US)
Pages (from-to)407-424
Number of pages18
JournalJournal of Differential Geometry
Volume74
Issue number3
DOIs
StatePublished - Jan 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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