Rotation Minimizing vector fields and frames in Riemannian manifolds

Abstract

We prove that a normal vector field along a curve in R3 is rotation minimizing (RM) if and only if it is parallel respect to the normal connection. This allows us to generalize all the results of RM vectors and frames to curves immersed in Riemannian manifolds.

References in corpus (2)

• Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces
• The Curvatures of Regular Curves and Euclidean Invariants of their Derivatives

Cited by in corpus (7)

• Moving frames and the characterization of curves that lie on a surface
• Rotation minimizing frames and spherical curves in simply isotropic and pseudo-isotropic 3-spaces
• 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 spherical curves
• Geometric properties of rotation minimizing vector fields along curves in Riemannian manifolds
• Rectifying-type curves and rotation minimizing frame $R_n$
• Characterization of manifolds of constant curvature by ruled surfaces