On bertrand supercurves in super-euclidean space

Abstract

Using Banach Grassmann algebra, given by Rogers, a new scalar product, a new definition of the orthogonality and of Frenet frame associated to supersmooth supercurve are introduced on the (m, n)-dimensional total super-Euclidean space. It is well known that a characteristic property of Bertrand curve is the existence of a linear relation between its curvature and torsion. In this study, definition of Bertrand supercurve in B-L(m+n) is given and also some theorems for Bertrand supercurve in B-L(4+4) are obtained.