Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57M50, 51M04, 51M09, 51M20

Retrieve articles in all journals with MSC: 57M50, 51M04, 51M09, 51M20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1111430-3
Keywords: Similarity class, geometric structure, hyperbolic geometry, moduli space
Article copyright: © Copyright 1993 American Mathematical Society