A characterization of spherical polyhedron surfaces

Details A characterization of spherical polyhedron surfaces A characterization of spherical polyhedron surfaces

2004-08-09

arxiv.org/abs/math/0408112v3

J. Differential. Geom., 74 (2006), no.3, 407-424.

Mathematics

Geometric Topology

15 pages, correction of typos and adding a few remarks

Scientific paper

A spherical polyhedron 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 polyhedron surface. This paper investigates these surfaces from the point of view of inner angles. A rigidity result is obtained. A characterization of spherical polyhedron surfaces in terms of the triangulation and the angle assignment is established.

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