Dual Spherical Elastica

Abstract

The solutions of the dual bending energy functionalon the dual unit sphere $\mathbb{S}^{2}\subset \mathbb{D}^{3}$ areinvestigated. Dual spherical elastica is characterized by the Euler-Lagrangeequation by using techniques of calculus of variation. The real and dualparts of this differential equation are solved by different methods. Dualspherical elastica is shown to correspond to the elastic strip constitutedby planar elastica in $\mathbb{R}^{3}$