The geodesic total curvature of spherical curves
Domenico Mucci, Alberto Saracco
TL;DR
This paper extends the explicit formula for geodesic total curvature from 2-sphere curves to higher-dimensional spheres, utilizing new integral-geometric formulas for spherical curves.
Contribution
It introduces a generalized explicit formula for geodesic total curvature applicable to high-dimensional spheres, expanding previous results limited to the 2-sphere.
Findings
Derived explicit formula for high-dimensional spherical curves
Developed new integral-geometric formulas for curvature analysis
Extended curvature analysis techniques to higher dimensions
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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · 3D Shape Modeling and Analysis · Advanced Differential Geometry Research