Study on periodic surfaces using their representations by integrals of conformal one-forms

使用共形一式积分表示的周期曲面研究

• 批准号: 22540064
• 负责人: MORIYA Katsuhiro
• 金额: $ 1.75万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540064/
• 关键词: 曲面; 幾何学; 微分幾何学; 周期的曲面; 可積分系; 変換; 正則関数; リーマン面; 周期; 閉形式; クリフォード代数; 四元数; 平均曲率一定曲面; ハミルトン的極小; ラグランジュ曲面; 共形; 積分表示

The correspondence between the Lopez-Ros deformation of a minimal surface in Euclidean (four-)space and the dressing transformations of two families of flat connections associated with a minimal surface was cleared by the joint work with Dr, Katrin Leschke.This result was presented in domestic or foreign conferences and seminars. A generalization of harmonic inverse mean curvature and their transforms was studied. The result was published in an international journal. An analog of the Schwarz lemma for super-conformal surfaces in four-dimenaional Euclidean space is obtained. A preprint about this result was written and submitted to an international journal. Generalizing the Riemann bilinear relation for holomorhphic one-forms, a condition for the existence of periodic surfaces was obtained. A preprint about this result was written and submitted to an international journal.

与 Katrin Leschke 博士的共同工作明确了欧几里得（四）空间中最小表面的 Lopez-Ros 变形与与最小表面相关的两个平面连接族的修整变换之间的对应关系。在国内或国外的会议和研讨会上。研究了调和逆平均曲率及其变换的推广。该结果发表在国际期刊上。获得了四维欧几里德空间中超共形表面的施瓦茨引理的模拟。关于这一结果的预印本已撰写并提交给一家国际期刊。将黎曼双线性关系推广到全纯一型，得到了周期曲面存在的条件。关于这一结果的预印本已撰写并提交给一家国际期刊。

项目成果

曲面上のベクトル値完全一次微分形式

曲面上的向量值完全一阶微分形式

• 发表时间: 2011
• 作者: Kurosu;Sanae and Moriya;Katsuhiro;Kokoro Tanaka;守屋 克洋;高瀬将道;高瀬将道;守屋 克洋;大黒顕司・高瀬将道;Katsuhiro Moriya;高瀬将道;Katsuhiro Moriya;Katsuhiro Moriya;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;Katsuhiro Moriya;守屋克洋
• 通讯作者: 守屋克洋

球面への調和写像に付随するtt^*束

tt^* 与调和映射到球体相关的束

• 发表时间: 2010
• 作者: Kurosu;Sanae and Moriya;Katsuhiro;Kokoro Tanaka;守屋 克洋;高瀬将道;高瀬将道;守屋 克洋;大黒顕司・高瀬将道;Katsuhiro Moriya;高瀬将道;Katsuhiro Moriya;Katsuhiro Moriya;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;Katsuhiro Moriya;守屋克洋;Katsuhiro Moriya;Katsuhiro Moriya;守屋克洋
• 通讯作者: 守屋克洋

Description of a mean curvature sphere of a surface by quaternionic holomorphic geometry

用四元数全纯几何描述表面的平均曲率球面

• 发表时间: 2012
• 期刊: RIMS Kokyuroku
• 作者: Kurosu;Sanae and Moriya;Katsuhiro;Kokoro Tanaka;守屋 克洋;高瀬将道;高瀬将道;守屋 克洋;大黒顕司・高瀬将道;Katsuhiro Moriya;高瀬将道;Katsuhiro Moriya
• 通讯作者: Katsuhiro Moriya

Surfaces of constant mean curvature with symmetry

具有对称性的恒定平均曲率曲面

• 发表时间: 2011
• 作者: Kurosu;Sanae and Moriya;Katsuhiro;Kokoro Tanaka;守屋 克洋;高瀬将道;高瀬将道;守屋 克洋;大黒顕司・高瀬将道;Katsuhiro Moriya;高瀬将道;Katsuhiro Moriya;Katsuhiro Moriya;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;Katsuhiro Moriya;守屋克洋;Katsuhiro Moriya
• 通讯作者: Katsuhiro Moriya

Transforms for neutral surfaces and timelike surfaces

中性表面和类时表面的变换

• 发表时间: 2011
• 作者: Kurosu;Sanae and Moriya;Katsuhiro;Kokoro Tanaka;守屋 克洋;高瀬将道;高瀬将道;守屋 克洋;大黒顕司・高瀬将道;Katsuhiro Moriya;高瀬将道;Katsuhiro Moriya;Katsuhiro Moriya;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;守屋克洋;Katsuhiro Moriya
• 通讯作者: Katsuhiro Moriya