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arXiv · 2105.03840

The geodesic total curvature of spherical curves

Domenico Mucci·Alberto Saracco
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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.

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Domenico Mucci, Alberto Saracco. 2021-05-09. The geodesic total curvature of spherical curves. https://arxiv.org/abs/2105.03840

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