Geometric Invariants of Non-smooth Framed Curves
摘要
We compare the Serret–Frenet frame with a relatively parallel adapted frame (RPAF) introduced by Bishop [6] 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.