Inelastic flows of curves in 4D Galilean space

Abstract

The flow of a curve is said to be inelastic, if in the former case, the arc-length is preserved, and in the latter case, if the intrinsic curvature is preserved. Physically, inelastic curve flow is characterized by the absence of any strain energy induced from the motion. In this paper, we investigate inextensible flows of curves in Galilean 4-space. Also, we give necessary and sufficient conditions for an inelastic curve flow are first expressed as a partial differential equation involving the curvature and torsion.