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 f1, f2, which encodes intrinsic information about the geometry of (M, g).
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