Curves in multiplicative equiaffine plane

Key Points

• The study introduces the concept of multiplicative equiaffine arc length, enhancing understanding of curve properties.
• New Frenet formulas are established, providing significant insight into the behavior of these specialized plane curves.
• Multiplicative equiaffine plane curves with constant curvature are classified, revealing their structural characteristics.
• These findings expand the theoretical framework of plane geometry, highlighting the uniqueness of multiplicative equiaffine curves.

Abstract