Abstract
In this paper we construct a natural geometric structure for the space of shapesof a star-shaped polygon. Roughly speaking we find: The set ofsimilarity classes of marked stars forms a hyperbolic right angle pentagon bundle over the space of external angle sets ofinscribed pentagons.The assignment of the shape of its fiber to each angle setforms a hyperbolic plane bundle over the Teichmiiller space of hyperbolic right angle pentagons. Any automorphism induced by renumbering is compatible with these geometric structures.
| Original language | English |
|---|---|
| Pages (from-to) | 845-851 |
| Number of pages | 7 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 117 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1993 Mar |
| Externally published | Yes |
Keywords
- Geometric structure
- Hyperbolic geometry
- Moduli space
- Similarity class
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics