各向同性几何中主曲率比为常数的曲面
微分几何
2025-10-17 v2
摘要
我们研究了在欧氏几何与单各向同性几何中具有恒定主曲率比的曲面，并在某些技术限制下（后两种情况仅在各向同性几何中）刻画了此类旋转曲面、管道曲面、直纹曲面、螺旋曲面与平移曲面。我们交织运用了微分几何的多种方法，包括线几何与李球几何、常微分方程以及初等代数几何。
引用
@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}
}
备注
40 pages, 7 figures; exposition has been improved, more references have been added, and a few typos have been fixed. Beitr Algebra Geom (2024)