2015年3月
Intrinsic properties of surfaces with singularities
INTERNATIONAL JOURNAL OF MATHEMATICS
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- 巻
- 26
- 号
- 4
- 開始ページ
- 154008
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1142/S0129167X1540008X
- 出版者・発行元
- WORLD SCIENTIFIC PUBL CO PTE LTD
In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in R-3 are Kossowski metrics, and the pull-back metrics of surfaces consisting only of cross cap singularities are Whitney metrics. Since the singular sets of Kossowski metrics are the union of regular curves on the domains of definitions, and Whitney metrics admit only isolated singularities, these two classes of metrics are disjoint. In this paper, we give several characterizations of intrinsic invariants of cuspidal edges and cross caps in these classes of metrics. Moreover, we prove Gauss-Bonnet type formulas for Kossowski metrics and for Whitney metrics on compact 2-manifolds.
- リンク情報
- ID情報
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- DOI : 10.1142/S0129167X1540008X
- ISSN : 0129-167X
- eISSN : 1793-6519
- Web of Science ID : WOS:000353295700009