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Geometric invariants of non-smooth framed curves

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arxiv 2301.03525 v1 pith:RHFRX5B6 submitted 2023-01-09 math.AP

Giulia Bevilacqua , Luca Lussardi , Alfredo Marzocchi This is my paper · ORCID
classification math.AP
keywords curvesframegeometricinvariantsrpafadaptedapplicationsapproaches
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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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