Journal of Differential Geometry

A characterization of spherical polyhedral surfaces

Feng Luo

Full-text: Open access

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.

Article information

Source
J. Differential Geom., Volume 74, Number 3 (2006), 407-424.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1175266233

Digital Object Identifier
doi:10.4310/jdg/1175266233

Mathematical Reviews number (MathSciNet)
MR2269784

Zentralblatt MATH identifier
1127.52032

Subjects
Primary: 57Mxx: Low-dimensional topology

Citation

Luo, Feng. A characterization of spherical polyhedral surfaces. J. Differential Geom. 74 (2006), no. 3, 407--424. doi:10.4310/jdg/1175266233. https://projecteuclid.org/euclid.jdg/1175266233


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