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アイテム
COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES
http://hdl.handle.net/20.500.12000/23589
http://hdl.handle.net/20.500.12000/235892ffbcf8f-acc9-407c-865d-7ef542827747
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
Vol24p001.pdf
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| Item type | デフォルトアイテムタイプ（フル）(1) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2012-03-01 | |||||||||
| タイトル | ||||||||||
| タイトル | COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES | |||||||||
| 言語 | en | |||||||||
| 作成者 |
Kamiyama, Yasuhiko
× Kamiyama, Yasuhiko
× 神山, 靖彦
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| アクセス権 | ||||||||||
| アクセス権 | open access | |||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
| 内容記述 | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | If X, a compact connected closed C^∞-surface with Euler-Poincaré characteristic _X(X), has a Riemannian metric, and if K : X → R is the Gauss-curvature and dV is the absolute value of the exterior 2-form which represents the volume, then according to the theorem of Gauss-Bonnet, which holds for orientable as well as non-orientable surfaces, (2π)/1 ∫_xKdV=_X(X). When X is the standard sphere or torus in R^3 , the Gaussian curvature is well-known and we can compute the left-hand side explicitly. Let X be a compact connected closed C^∞-surface of any genus. In this paper, we construct an embedding of X into R^3 or R^4 according as X is orientable or nonorientable. We equip X with the Riemannian metric as a Riemannian submanifold of R^3 or R^4. Then, with the aid of a computer, we compute the left-hand side numerically for the cases that the genus of X is small. The computer data are sufficiently nice and coincide with the right-hand side without errors. Such nice data are obtained by converting double integrals to infinite integrals. | |||||||||
| 内容記述 | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | 紀要論文 | |||||||||
| 出版者 | ||||||||||
| 出版者 | Department of Mathematical Science, Faculty of Science, University of the Ryukyus | |||||||||
| 言語 | en | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | departmental bulletin paper | |||||||||
| 出版タイプ | ||||||||||
| 出版タイプ | NA | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_be7fb7dd8ff6fe43 | |||||||||
| 識別子 | ||||||||||
| 識別子 | http://hdl.handle.net/20.500.12000/23589 | |||||||||
| 識別子タイプ | HDL | |||||||||
| 収録物識別子 | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 1344-008X | |||||||||
| 収録物識別子 | ||||||||||
| 収録物識別子タイプ | NCID | |||||||||
| 収録物識別子 | AA10779580 | |||||||||
| 収録物名 | ||||||||||
| 収録物名 | Ryukyu mathematical journal | |||||||||
| 言語 | en | |||||||||
| 書誌情報 |
巻 24, p. 1-17, 発行日 2011-12 |
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