Surfaces of constant principal-curvatures ratio in isotropic geometry

2023/07/12 by Yorov, Khusrav, Skopenkov, Mikhail, Pottmann, Helmut · 1 citation
#53A05 #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.05968

Abstract

We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational surfaces of this kind under some technical restrictions (the latter two cases only in isotropic geometry). We use the interlacing of various methods of differential geometry, including line geometry and Lie sphere geometry, ordinary differential equations, and elementary algebraic geometry.

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• Families of surfaces with constant ratio of principal curvatures and Plateau's problem

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