Geometric invariants of non-smooth framed curves

2023/01/09 by Giulia Bevilacqua, Bevilacqua, Giulia, Luca Lussardi +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #53A04 #74B20 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Dermatological and Skeletal Disorders #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2301.03525

openalex publication_date 2023/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Cited by

• The fundamental theorem of the local theory for non-smooth curves

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