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math.DG2023
Total torsion of three-dimensional lines of curvature
Matteo Raffaelli
A curve in a Riemannian manifold is three-dimensional if its torsion (signed second curvature function) is well-defined and all higher-order curvatures vanish identically.…
math.DG2023★ 1 cited
Existence of optimal flat ribbons
Simon Blatt, Matteo Raffaelli
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in can be extended to an infinitely narrow flat ribbon having mini…