Classification of Möbius homogeneous curves in R4

Tongzhu Li; Ruiyang Lin

doi:10.3934/math.20241119

Classification of Möbius homogeneous curves in R⁴

Tongzhu Li^*, Ruiyang Lin

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

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.

Original language	English
Pages (from-to)	23027-23046
Number of pages	20
Journal	AIMS Mathematics
Volume	9
Issue number	8
DOIs	https://doi.org/10.3934/math.20241119
Publication status	Published - 2024

Keywords

Möbius arclength
Möbius curvature
Möbius homogeneous curve
Möbius transformation group

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10.3934/math.20241119

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abstract = "In this paper, we investigate the M{\"o}bius geometry of curves in R4. First, using moving frame methods we construct a complete system of M{\"o}bius invariants for regular curves in R4 by the isometric invariants. Second, we completely classify the M{\"o}bius homogeneous curves in R4 up to a M{\"o}bius transformation of R4.",

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AU - Li, Tongzhu

AU - Lin, Ruiyang

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AB - 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.

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KW - Möbius curvature

KW - Möbius homogeneous curve

KW - Möbius transformation group

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Classification of Möbius homogeneous curves in R⁴

Abstract

Keywords

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