Surfaces of constant principal-curvatures ratio in isotropic geometry

Khusrav Yorov; Mikhail Skopenkov; Helmut Pottmann

doi:10.1007/s13366-024-00768-5

Surfaces of constant principal-curvatures ratio in isotropic geometry

Khusrav Yorov, Mikhail Skopenkov^*, Helmut Pottmann

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Journal	Beitrage zur Algebra und Geometrie
DOIs	https://doi.org/10.1007/s13366-024-00768-5
State	Accepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Managing Editors 2024.

Keywords

53A05
53A10
53C42
Constant ratio of principal curvatures
Isotropic geometry
Minimal surfaces
Weingarten surfaces

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s13366-024-00768-5

Cite this

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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.",

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KW - 53A10

KW - 53C42

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KW - Isotropic geometry

KW - Minimal surfaces

KW - Weingarten surfaces

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Surfaces of constant principal-curvatures ratio in isotropic geometry

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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