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2022 Fiscal Year Annual Research Report

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

Research Project

Project/Area Number 22F22701
Allocation TypeSingle-year Grants
Research InstitutionKobe University

Principal Investigator

Rossman W.F  神戸大学, 理学研究科, 教授 (50284485)

Co-Investigator(Kenkyū-buntansha) POLLY DENIS  神戸大学, 理学研究科, 外国人特別研究員
Project Period (FY) 2022-07-27 – 2024-03-31
Keywordsdiscrete surfaces / integrable systems / transformation theory / Lie sphere geometry
Outline of Annual Research Achievements

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.

Research Progress Status

翌年度、交付申請を辞退するため、記入しない。

Strategy for Future Research Activity

翌年度、交付申請を辞退するため、記入しない。

  • Research Products

    (6 results)

All 2023 2022

All Journal Article (2 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 2 results) Presentation (4 results) (of which Int'l Joint Research: 2 results,  Invited: 4 results)

  • [Journal Article] Discrete Weierstrass-type representations2023

    • Author(s)
      Mason Pember, Denis Polly, Masashi Yasumoto
    • Journal Title

      Discrete Comput Geom

      Volume: to appear Pages: --

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Channel linear Weingarten surfaces in space forms2023

    • Author(s)
      Udo Hertrich-Jeromin, Mason Pember, Denis Polly
    • Journal Title

      Beitr Algebra Geom

      Volume: to appear Pages: --

    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Rotational cmc surfaces in space forms2023

    • Author(s)
      Denis Polly
    • Organizer
      Korea 3rd Conference on Surfaces, Analysis, and Numerics
    • Int'l Joint Research / Invited
  • [Presentation] Discrete Weierstrass-type representations2022

    • Author(s)
      Denis Polly
    • Organizer
      Geometry Seminar, Tokyo Institute of Technology
    • Invited
  • [Presentation] Discrete channel linear Weingarten surfaces2022

    • Author(s)
      Denis Polly
    • Organizer
      Discrete Geometric Structures 2022
    • Invited
  • [Presentation] Representations of Discrete Bryant type surfaces2022

    • Author(s)
      Denis Polly
    • Organizer
      13th MSJ-SI "Differential Geometry and Integrable systems
    • Int'l Joint Research / Invited

URL: 

Published: 2023-12-25  

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