Surfaces of constant principal-curvatures ratio in isotropic geometry

被引：1
作者：
Yorov, Khusrav [1 ]
Skopenkov, Mikhail [1 ]
Pottmann, Helmut [1 ,2 ]
机构：
[1] King Abdullah Univ Sci & Technol, Thuwal 23955, Saudi Arabia
[2] Vienna Univ Technol, Vienna, Austria
来源：
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2024年
关键词：
Isotropic geometry; Constant ratio of principal curvatures; Minimal surfaces; Weingarten surfaces; TRANSLATION SURFACES; SPACE;
D O I：
10.1007/s13366-024-00768-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页数：40
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