Backlund transformations of curves in the Galilean and pseudo-Galilean spaces

TL;DR

This paper investigates Backlund transformations of curves in Galilean and pseudo-Galilean spaces, showing they preserve torsion under specific conditions, thus extending geometric transformation theory in non-Euclidean geometries.

Contribution

It introduces new Backlund transformations for curves in Galilean and pseudo-Galilean spaces and analyzes their torsion-preserving properties.

Findings

Transformations preserve torsion under certain assumptions

Backlund transformations extend to spatial curves in Galilean 4-space

Results contribute to geometric transformation theory in non-Euclidean spaces

Abstract

Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.