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Discrete differential geometry, Lie sphere geometry, discrete surfaces theory, surface representations

离散微分几何、李球几何、离散曲面理论、曲面表示

基本信息

批准号：
22KF0255
负责人：
Rossman W.F
金额：
$ 0.7万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2023
资助国家：
日本
起止时间：
2023-03-08 至 2024-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22KF0255/
关键词：
discrete surfaces integrable systems transformation theory Lie sphere geometry

项目摘要

During this fiscal year, Denis Polly used this grant to conduct research in discrete differential geometry. One project is on discrete constant mean curvature 1 surfaces in hyperbolic 3-space, including also myselfand Denis and Udo Hertrich-Jeromin of Vienna Technical University and Andrew Sageman-Furnas of North Carolina State University. Another project is on linear Weingarten surfaces that are also Lie minimal, including also Masaya Hara and Tomohiro Tada of Kobe University, and Joseph Cho of TU-Vienna.Denis also worked with other researchers at other universities in Japan, such as Masashi Yasumoto and Tokushima University, and has potential projects developing as a result.In the first of the two projects, he succeeded in extending the notion of edge-constraint to associated families of discrete constant mean curvature 1 surfaces in hyperbolic 3-space. This is significant because up until now the notion of edge-constraint has been applied only to surfaces in Euclidean 3-space.In the second project, it has been shown that any minimal or constant mean curvature or affine linear Weingarten surfaces in Euclidean 3-space that is also Lie minimal must be a surface of revolution, and that the situation is slightly more complicated in the case of surfaces in a non-Euclidean spaceform.

在本财政年度，丹尼斯波利用这笔赠款进行研究离散微分几何。一个项目是离散的常平均曲率1曲面在双曲3空间，也包括myselfand丹尼斯和乌多赫里奇杰罗明的维也纳技术大学和安德鲁萨格曼Furnas的北卡罗来纳州州立大学。另一个项目是关于线性Weingarten曲面也是Lie最小的，包括科比大学的马萨亚Hara和Tomohiro Tada，以及TU-Vienna的Joseph Cho。Denis还与日本其他大学的其他研究人员合作，如Masashi Yasumoto和德岛大学，并因此开发了潜在的项目。在两个项目的第一个中，他成功地将边约束的概念推广到双曲3-空间中离散的常平均曲率1曲面的相关族。这是重要的，因为到目前为止，边约束的概念只适用于欧氏空间中的曲面。在第二个项目中，它已被证明，任何最小或常数平均曲率或仿射线性Weingarten曲面在欧氏空间中，也是李极小必须是一个表面的革命，而这种情况是稍微复杂的情况下，表面在非欧氏空间形式。