English

The geodesic total curvature of spherical curves

Differential Geometry 2023-03-13 v2

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

Cite

@article{arxiv.2105.03840,
  title  = {The geodesic total curvature of spherical curves},
  author = {Domenico Mucci and Alberto Saracco},
  journal= {arXiv preprint arXiv:2105.03840},
  year   = {2023}
}

Comments

Unluckily we found an error in one proof