A New Version of Energy and Elastica for Curves with Extended Darboux Frame

Abstract

In this work, we research geometrical interpretation involved with the energy by ED-frame field of first and second kind on an orientable hypersurface in E4. We explore the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for ED-frame field of first and second kind. Moreover, we have an original and satisfactorily association among energy of the curve on orientable hypersurface in E4.