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arXiv · 1007.2960

The Curvatures of Regular Curves and Euclidean Invariants of their Derivatives

Eugene Gutkin
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Abstract

The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in $R^n$ is determined up to an isometry by the norms of its n derivatives. We extend these observations to curves in arbitrary riemannian manifolds.

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Eugene Gutkin. 2010-07-17. The Curvatures of Regular Curves and Euclidean Invariants of their Derivatives. https://doi.org/10.1016/j.geomphys.2011.06.013

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