On discrete constant principal curvature surfaces

Author:

Y. Kabata, S. Matsutani, Y. Ogata

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Mathematical Physics (math-ph)

journal:

date:

2023-06-27 16:00:00

Abstract

Recently, it is discovered that a certain class of nanocarbon materials has geometrical properties related to the discrete geometry, pre-constant discrete principal curvature [9] based on the discrete surface theory proposed on trivalent graphs by Kotani, Naito and Omori [10]. In this paper, with the aim of an application to the nanocarbon materials, we will study discrete constant principal curvature (CPC) surfaces. Firstly, we developed the discrete surface theory on a full 3-ary oriented tree so that we define a discrete analogue of principal directions on them to investigate it. We also construct some interesting examples of discrete constant principal curvature surfaces, including discrete CPC tori.

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