Classification of ruled surfaces with non-degenerate second fundamental forms in Lorentz-Minkowski 3-spaces

Abstract

In this paper, we study some properties of ruled surfaces in a three-dimensional Lorentz-Minkowski space related to their Gaussian curvature, the second Gaussian curvature and the mean curvature. Furthermore, we examine the ruled surfaces in a three-dimensional Lorentz-Minkowski space satisfying the Jacobi condition formed with those curvatures, which are called the H-W and the H-G ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.