Original Article
Kyungpook Mathematical Journal 2007; 47(4): 579-593
Published online December 23, 2007
Copyright © Kyungpook Mathematical Journal.
Classiffcation of Ruled Surfaces with Non-degenerate Second Fundamental Forms in Lorentz-Minkowski 3-Spaces
Sunmi Jung1, Young Ho Kim1, Dae Won Yoon2
1Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea
2Department of Mathematics, College of Education and RINS, Gyeongsang National University, Chinju, 660-701, Korea
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 {it II-W} and the {it II-G} ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.
Keywords: Lorentz-Minkowski space, Ruled surface, Second Gaussian curvature, Mean curvature, Gaussian curvature, $II$-$W$ and $II$-$G$ ruled surface