Elastic strips along isotropic curves in complex 3-spaces

Abstract

In this paper, we define the ruled surface in terms of the Darboux vector field of an isotropic curve in a complex 3 -space, and we study the ruled surface as an elastic strip along the isotropic curve. First of all, we show that elastic strips along isotropic curves that serve critical points of the modified Sadowsky functional are characterized by three Euler-Lagrange equations. As a result, we give two conservation laws to characterize elastic strips of isotropic curves in complex 3 -space and explain an isotropic helix in terms of the force vector. Finally, we give some examples to illustrate elastic strips with isotropic curves in a complex 3 -space.