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  1. 紀要論文
  2. Ryukyu mathematical journal
  3. 24巻
  1. 部局別インデックス
  2. 理学部

COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES

http://hdl.handle.net/20.500.12000/23589
http://hdl.handle.net/20.500.12000/23589
2ffbcf8f-acc9-407c-865d-7ef542827747
名前 / ファイル ライセンス アクション
Vol24p001.pdf Vol24p001.pdf
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

en Kamiyama, Yasuhiko

神山, 靖彦

× 神山, 靖彦

ja 神山, 靖彦

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.
内容記述タイプ Other
内容記述 紀要論文
出版者
言語 en
出版者 Department of Mathematical Science, Faculty of Science, University of the Ryukyus
言語
言語 eng
資源タイプ
資源タイプ departmental bulletin paper
資源タイプ識別子 http://purl.org/coar/resource_type/c_6501
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
収録物識別子タイプ NCID
収録物識別子 AA10779580
収録物名
言語 en
収録物名 Ryukyu mathematical journal
書誌情報
巻 24, p. 1-17
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