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arXiv · 2203.11811

The geometry of Riemannian curvature radii

Eugenio Bellini
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Abstract

In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold $(M, g)$. We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and we investigate their properties. The main character of our construction is a pair of global vector fields $f_1, f_2$, which encodes intrinsic information about the geometry of $(M, g)$.

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Eugenio Bellini. 2022-03-22. The geometry of Riemannian curvature radii. https://doi.org/10.1007/s10883-023-09664-y

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