Inserted: 7 may 2021
Last Updated: 7 may 2021
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