Geometric invariants of non-smooth framed curves

Giulia Bevilacqua; Luca Lussardi; Alfredo Marzocchi

Geometric invariants of non-smooth framed curves

Analysis of PDEs 2023-01-10 v1

Authors: Giulia Bevilacqua , Luca Lussardi , Alfredo Marzocchi

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.

Keywords

framed curves serret-frenet frame relatively parallel adapted frame geometric invariants curvature torsion variational problems

Cite

@article{arxiv.2301.03525,
  title  = {Geometric invariants of non-smooth framed curves},
  author = {Giulia Bevilacqua and Luca Lussardi and Alfredo Marzocchi},
  journal= {arXiv preprint arXiv:2301.03525},
  year   = {2023}
}