### 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 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Geometric structure
- Hyperbolic geometry
- Moduli space
- Similarity class

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Shapes of stars.** / Kojima, Sadayoshi.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 117, no. 3, pp. 845-851. https://doi.org/10.1090/S0002-9939-1993-1111430-3

}

TY - JOUR

T1 - Shapes of stars

AU - Kojima, Sadayoshi

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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.

AB - 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.

KW - Geometric structure

KW - Hyperbolic geometry

KW - Moduli space

KW - Similarity class

UR - http://www.scopus.com/inward/record.url?scp=0000369162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000369162&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1993-1111430-3

DO - 10.1090/S0002-9939-1993-1111430-3

M3 - Article

AN - SCOPUS:0000369162

VL - 117

SP - 845

EP - 851

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -