ガウス写像の性質に基づく曲面の大域的性質の研究

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Author: 川上, 裕ほか

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Publication date: 2015-06-12

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Note (General)：: 金沢大学理工研究域数物科学系３次元ユークリッド空間内の極小曲面や３次元アファイン空間内の非固有アファイン球面，３次元双曲型空間内の平坦曲面といったさまざまな曲面のクラスにおけるガウス写像の函数論的性質の幾何学的意味を明らかにした．特に，開リーマン面上のある等角計量のガウス曲率の評価を与え，その応用と...

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https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-24740044/24740044seika/

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Material Type: 文書・図像類
Title: ガウス写像の性質に基づく曲面の大域的性質の研究
Author/Editor: 川上, 裕
Kawakami, Yu
Author Heading: 川上, 裕
Kawakami, Yu
Publication Date: 2015-06-12
Publication Date (W3CDTF): 2015-06-12
Alternative Title: A study on the relationship between the global property of immered surfaces in space forms and the behavior of their Gauss maps
Periodical title: 平成26(2014)年度科学研究費補助金若手研究(B) 研究成果報告書 = 2014 Fiscal Year Final Research Report
No. or year of volume/issue: 2012-04-01 - 2015-03-31
Volume: 2012-04-01 - 2015-03-31
Pages: 4p.-
Text Language Code: jpn
Subject Heading: 幾何学
函数論
曲面論
値分布論
ガウス写像
波面（フロント）
除外値
一意性定理
Target Audience: 一般
Note (General): 金沢大学理工研究域数物科学系
３次元ユークリッド空間内の極小曲面や３次元アファイン空間内の非固有アファイン球面，３次元双曲型空間内の平坦曲面といったさまざまな曲面のクラスにおけるガウス写像の函数論的性質の幾何学的意味を明らかにした．特に，開リーマン面上のある等角計量のガウス曲率の評価を与え，その応用として，完備性を満たすときのこれらの曲面のガウス写像の除外値数の上限の幾何学的意味を明らかにした．
We elucidated the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the affine three-space and flat surfaces in hyperbolic three-space. In particular, we give an effective curvature bound for a specified conformal metric on an open Riemann surface. As an application of the result, we revealed the geometric meaning of the maximal number of exceptional values of Gauss maps for these surfaces.
研究課題/領域番号:24740044, 研究期間(年度):2012-04-01 - 2015-03-31
DOI: 10.24517/00052348
Access Restrictions: 限定公開
Related Material: https://kaken.nii.ac.jp/search/?qm=60532356
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24740044/
https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-24740044/24740044seika/
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 金沢大学 : 金沢大学学術情報リポジトリKURA