抄録
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.
| 元の言語 | English |
|---|---|
| ページ（範囲） | 845-851 |
| ページ数 | 7 |
| ジャーナル | Proceedings of the American Mathematical Society |
| 巻 | 117 |
| 発行部数 | 3 |
| DOI | |
| 出版物ステータス | Published - 1993 1 1 |
| 外部発表 | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
これを引用
Shapes of stars. / Kojima, Sadayoshi.
：: Proceedings of the American Mathematical Society, 巻 117, 番号 3, 01.01.1993, p. 845-851.研究成果: Article
}
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
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 -