Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Shapes of stars

Authors: Sadayoshi Kojima and Yasushi Yamashita
Journal: Proc. Amer. Math. Soc. 117 (1993), 845-851
MSC: Primary 57M50; Secondary 51M04, 51M09, 51M20
MathSciNet review: 1111430
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Abstract: In this paper we construct a natural geometric structure for the space of shapes of a star-shaped polygon. Roughly speaking we find: The set of similarity classes of marked stars forms a hyperbolic right angle pentagon bundle over the space of external angle sets of inscribed pentagons. The assignment of the shape of its fiber to each angle set forms a hyperbolic plane bundle over the Teichmüller space of hyperbolic right angle pentagons. Any automorphism induced by renumbering is compatible with these geometric structures.

References [Enhancements On Off] (What's this?)

  • [1] Makoto Sakuma, The geometries of spherical Montesinos links, Kobe J. Math. 7 (1990), no. 2, 167–190. MR 1096689
  • [2] W. P. Thurston, Shapes of polyhedra, preprint, 1987.

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Keywords: Similarity class, geometric structure, hyperbolic geometry, moduli space
Article copyright: © Copyright 1993 American Mathematical Society