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 Kähler manifold.

To appear in Turkish Journal of Mathematics

References in corpus (1)

• Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces

Cited by in corpus (2)

• Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere
• Characterization of manifolds of constant curvature by ruled surfaces