離散曲線のDarboux変換を用いた双等温曲面の構成法

• Project/Area Number: 24K06722
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11020:Geometry-related
• Research Institution: Kyoto Sangyo University
• Principal Investigator: 緒方 勇太 京都産業大学, 理学部, 准教授 (50800801)
• Project Period (FY): 2024-04-01 – 2028-03-31
• Project Status: Granted (Fiscal Year 2024)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2027: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2026: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2025: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2024: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: Darboux変換 / 離散微分幾何学

Outline of Research at the Start

「離散曲線のDarboux変換」を用いて新たな双等温曲面の構成を目指し，研究活動を行う．具体的には，離散曲線のDarboux変換に対する「Bianchiの可換律」の証明，「離散双等温トーラス」の構成，連続極限による「双等温トーラス」の構成が目標である．