On the governing equations of membrane O surfaces

2025/10/22 by Yoshiki Jikumaru, Jikumaru, Yoshiki
Engineering · Mathematics · #37K35 #53A05 #53C42 #74K15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2510.19284

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

It is known that a shell membrane in equilibrium where a constant purely normal load q_n acts on the membrane, and where the principal curvature lines coincide with the principal stress lines, forms an integrable system called a membrane O surface. This paper formulates the governing equations for membrane O surfaces of the 1st and 2nd kind, which are analogues to Guichard surfaces of the 1st and 2nd kind introduced by Calapso. Furthermore, under this formulation, we show that membrane O surfaces are a subclass of Demoulin's Ω surfaces, and that the Bäcklund transformation for membrane O surfaces preserves membrane O surfaces of the 1st and 2nd kind, respectively.

Citations

• On the unification of classical and novel integrable surfaces: I. Differential geometry

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