Null parallel p-equidistant b-scrolls

Abstract

In this paper, null parallel p-equidistant B-scrolls are defined in 3-dimensional Minkowski space  R_1^3 . We prove necessary and sufficient conditions for these B-scrolls to be equivalent of their Cartan frames. The relations between matrices of the shape operators and the algebraic invariants (Gauss, mean curvatures, principal curvatures) of these B-scrolls are shown. Besides we give the relations between second Gauss curvatures, mean curvatures and the distribution parameters of non-developable null parallel p-equidistant B-scrolls. Finally, an example is given related to the null parallel p-equidistant B-scrolls in  R_1^3.