Weingarten type ruled surfaces and skew curvatures in Minkowski 3-space

Abstract In this paper, we study the skew curvature of ruled surface in Minkowski 3-space. The skew curvature is closely related to quantum mechanics in the study of the dynamics, and is derived from Schrödinger equation on a surface. First of all, we prove that there is no linear Weingarten type ruled surfaces with non-null ruling in terms of the Gaussian, mean and skew curvatures. Also, we show that the ruled surface with null ruling (shortly, null scroll) has zero skew curvature. Finally, we give an application to construct null scrolls with zero skew curvature.