Lamarle formula in 3-dimensional Lorentz space

Abstract

The Lamarle Formula is known as a relationship between the Gaussian curvature and the distribution parameter (Drall) of a ruled surface in the surface theory, [12]. In R-1(3), the non-null ruled surfaces were investigated in five different classes with respect to the character of base curves and rulings, [8]-[10]. In this paper, by excluding the null tangent of ruling, three different kinds of non-null ruled are taken into consideration and the relationships between the Gaussian curvatures and distribution parameters of spacelike ruled surface, timelike ruled surface with spacelike ruling and timelike ruled surface with timelike ruling are obtained, respectively. These relationships are called as Lorentzian Lamarle formulae. Finally, some examples concerning these relations are given.