Biminimal curves in euclidean spaces

Abstract

We study with biminimal curves, that is curves which are critical points of the bienergy for normal variations. We give a description of the Euler-Lagrange equation associated to biminimal curves on a Riemannian manifold. We describe curves of AW(k) type of Euclidean n-space E-n. We show that every biminimal curves of E-n are of AW(1)-type. We also show that lambda-biminimal curves of E-n are of AW(3)-type.