Surfaces of constant principal-curvatures ratio in isotropic geometry
arXiv:2307.05968 · doi:10.1007/s13366-024-00768-5
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.
40 pages, 7 figures; exposition has been improved, more references have been added, and a few typos have been fixed. Beitr Algebra Geom (2024)