Geometric invariants of non-smooth framed curves

Published 9 Jan 2023 in math.AP | (2301.03525v1)

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.

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