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Research Article | Open Access

Classification of Möbius homogeneous curves in R4

Tongzhu Li1( ), Ruiyang Lin1,2
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Beijing Key Laboratory on MCAACI, Beijing 100081, China
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Abstract

In this paper, we investigate the Möbius geometry of curves in R4. First, using moving frame methods we construct a complete system of Möbius invariants for regular curves in R4 by the isometric invariants. Second, we completely classify the Möbius homogeneous curves in R4 up to a Möbius transformation of R4.

Keywords

Möbius transformation groupMöbius homogeneous curveMöbius arclengthMöbius curvature
CLC number: 53A04, 53A31

References

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 23027-23046
DOI: 10.3934/math.20241119

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Li T, Lin R. Classification of Möbius homogeneous curves in R4. AIMS Mathematics, 2024, 9(8): 23027-23046. https://doi.org/10.3934/math.20241119

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Received: 25 May 2024
Revised: 09 July 2024
Accepted: 18 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)