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
相关论文
共 64 条
[1]   Reflection Principles for Zero Mean Curvature Surfaces in the Simply Isotropic 3-space [J].
Akamine, Shintaro ;
Fujino, Hiroki .
RESULTS IN MATHEMATICS, 2022, 77 (04)
[2]   Classifications of Translation Surfaces in Isotropic Geometry with Constant Curvature [J].
Aydin, M. E. .
UKRAINIAN MATHEMATICAL JOURNAL, 2020, 72 (03) :329-347
[3]  
Aydin ME, 2017, INT ELECTRON J GEOM, V10, P21
[4]  
Aydn ME., 2016, Afyon Kocatepe Univ. J. Sci. Eng, V16, P239
[5]  
Blaschke W., 1929, Differentialgeometrie 3: Differentialgeometrie der Kreise und Kugeln
[6]  
Bruce J. W., 1984, CURVES SINGULARITIES
[7]  
da Silva LCB., 2021, Math. J. Okayama Univ, V63, P15, DOI [10.18926/mjou/60864, DOI 10.18926/MJOU/60864]
[8]   Catenaries and Singular Minimal Surfaces in the Simply Isotropic Space [J].
da Silva, Luiz C. B. ;
Lopez, Rafael .
RESULTS IN MATHEMATICS, 2023, 78 (05)
[9]   Holomorphic representation of minimal surfaces in simply isotropic space [J].
da Silva, Luiz C. B. .
JOURNAL OF GEOMETRY, 2021, 112 (03)
[10]  
Giering O., 1982, Vorlesungen ber Hhere Geometrie, DOI [10.1007/978-3-322-83552-9, DOI 10.1007/978-3-322-83552-9]
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