Development of analysis and discretization in differential geometry

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K03585
• 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: Kobe University
• Principal Investigator: Rossman W. F 神戸大学, 理学研究科, 教授 (50284485)
• Co-Investigator(Kenkyū-buntansha): 安本 真士 徳島大学, 大学院社会産業理工学研究部(理工学域), 講師 (70770543)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: differential geometry / surface theory / transformation theory / surface representations / Lie sphere geometry / discrete surfaces / Moebius geometry / integrable systems

Outline of Final Research Achievements

This research focused on the many structures that smooth surfaces have, and on maintaining this structure in the discrete analogues within surface theory. The following three issues were addressed: firstly, the study of how singularities appearing on surfaces are related to the properties of integrable systems of surfaces; secondly, the study of mathematical properties appearing in the construction of larger classes of discrete surfaces; thirdly, the study of smooth surfaces possibly having singularities and changes in their metric signature, by the methods of integrable systems.

Free Research Field

differential geometry

Academic Significance and Societal Importance of the Research Achievements

この研究の意義は、滑らかな曲面と離散曲面が持つ数学的構造のさらなる解明と理解の促進や、離散微分幾何学を研究するベルリン工科大学、ウィーン工科大学、イギリスのバース大学との連携を深めることにあります。
English translation: The significance is to further promote understanding of smooth and discrete surfaces, and to promote discrete differential geometry, and to deepen international collaboration.