Accepted Paper

Inserted: 10 jan 2023
Last Updated: 23 jan 2024

Journal: INdAM Springer Series
Year: 2023

Abstract:

We compare the Serret-Frenet frame with a {\em relatively parallel adapted frame} (RPAF) introduced by Bishop to parametrize $W^{2,2}$-curves. Next, we derive the geometric invariants, curvature and torsion, with the RPAF associated to the curve. Finally, we discuss applications of the two approaches in variational problems.