Differential geometric approach to discrete surfaces

2022 Fiscal Year Final Research Report

• Project/Area Number: 15K04845
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kobe University
• Principal Investigator: ROSSMAN W. F 神戸大学, 理学研究科, 教授 (50284485)
• Co-Investigator(Kenkyū-buntansha): 直川 耕祐 神戸大学, 理学研究科, 特別研究員(PD) (60740826) ; 佐治 健太郎 神戸大学, 理学研究科, 教授 (70451432)
• Project Period (FY): 2015-04-01 – 2023-03-31
• Keywords: differential geometry / surface theory / transformation theory / surface representations / Lie sphere geometry / discrete surfaces

Outline of Final Research Achievements

This was research on extending the rich mathematical structure of smooth surfaces to discretized surfaces, including studies of A) how singular behavior of various types on surfaces manifests itself within associated integrable systems, B) new methods of constructing discrete surfaces, and analysis of the properties that appear, C) smooth surfaces with integrable systems properties that can have singularities and/or signature type change.

Free Research Field

differential geometry

Academic Significance and Societal Importance of the Research Achievements

この研究の意義は離散曲面に関連する構造と性質の理解を深めることや、ベルリン工科大学、ウィーン工科大学、イギリスのバース大学といった離散曲面理論研究グループとの連携を深めることにあります。[English translation: This research creates expanded understanding of the structures of discrete surfaces, connecting with research groups at Berlin and Vienna Technical Universities, and Bath University.