Calculus of Variations and Geometric Measure Theory
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D. Mucci - A. Saracco

The geodesic total curvature of spherical curves

created by mucci on 07 May 2021

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Submitted Paper

Inserted: 7 may 2021
Last Updated: 7 may 2021

Year: 2021

Abstract:

The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of some new integral-geometric formulas concerning both the Euclidean and geodesic total curvature of spherical curves.

Keywords: Spherical curves, Geodesic curvature, Integral-geometric formulas, Non-smooth curves


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