Surfaces of constant principal-curvatures ratio in isotropic geometry
Differential Geometry
2025-10-17 v2
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.
Keywords
Cite
@article{arxiv.2307.05968,
title = {Surfaces of constant principal-curvatures ratio in isotropic geometry},
author = {Khusrav Yorov and Mikhail Skopenkov and Helmut Pottmann},
journal= {arXiv preprint arXiv:2307.05968},
year = {2025}
}
Comments
40 pages, 7 figures; exposition has been improved, more references have been added, and a few typos have been fixed. Beitr Algebra Geom (2024)