The geometry of Riemannian curvature radii

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 $(M,g)$.

arXiv comment36 pages

References in corpus (1)

• Bicycle paths, elasticae and sub-Riemannian geometry