Geometric properties of rotation minimizing vector fields along curves in Riemannian manifolds

Abstract

Rotation minimizing vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed into a Riemannian manifold are studied when the ambient manifold is the Euclidean 3-space, the Hyperbolic 3-space and a K\"{a}hler manifold.