Yorov, K., Skopenkov, M., & Pottmann, H. (2024). Surfaces of constant principal-curvatures ratio in isotropic geometry. Beitraege Zur Algebra Und Geometrie. https://doi.org/10.1007/s13366-024-00768-5
53A05; 53A10; 53C42; Constant ratio of principal curvatures; Isotropic geometry; Minimal surfaces; Weingarten surfaces
en
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.
