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; 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博士的关节工作清除了欧几里得（四个）空间中最小表面（四个）空间中最小表面的洛杉矶变形与两个与最低表面相关的平坦连接家族的敷料转化之间的对应关系。这在家庭或外国会议和扬声器中呈现了这一结果。研究了谐波反向平均曲率及其变换的概括。结果发表在国际杂志上。获得了四维欧几里得空间中超符号表面的Schwarz引理的类似物。关于此结果的预印本被编写并提交给国际日报。概括了Riemann双线性关系以进行全体型单型，因此获得了周期性表面的存在条件。关于此结果的预印本被编写并提交给国际日报。