Classification of Möbius homogeneous curves in $ \mathbb{R}^4 $

Abstract

In this paper, we investigate the Möbius geometry of curves in $ \mathbb{R}^4 $. First, using moving frame methods we construct a complete system of Möbius invariants for regular curves in $ \mathbb{R}^4 $ by the isometric invariants. Second, we completely classify the Möbius homogeneous curves in $ \mathbb{R}^4 $ up to a Möbius transformation of $ \mathbb{R}^4 $.

Keywords

• möbius transformation group
• möbius homogeneous curve
• möbius arclength
• möbius curvature