Published Paper

Inserted: 10 jan 2023
Last Updated: 1 feb 2025

Journal: INdAM Springer Series
Pages: 1-13
Year: 2024
Doi: https://doi.org/10.1007/978-981-97-6984-1_1

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.