2023/06/28 by Yutaro Kabata, Kabata, Y., Shigeki Matsutani +3
Computer Science · Mathematics · #53A70(Primary) #74A30(Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Graph theory and applications #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2306.15846
openalex publication_date 2023/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.