Kim, Young Ho; Yoon, Dae Won Classification of ruled surfaces in Minkowski 3-spaces. (English) Zbl 1078.53006 J. Geom. Phys. 49, No. 1, 89-100 (2004). For a surface without points of vanishing Gaussian curvature, in a 3-dimensional Minkowski space \(E_{1}^{3}\) the second Gaussian curvature is defined formally. In the present article the authors classify the non-developable ruled surfaces in \(E_{1}^{3}\) for which a linear combination between two of the quantities, the Gaussian curvature \(K\), the second Gaussian curvature \(K_{II}\) and the mean curvature \(H\), is constant along the rulings. An analogous classification for surfaces in the Euclidean space was obtained by D. E. Blair and T. Koufogiorgos [Monatsh. Math. 113, No. 3, 177–181 (1992; Zbl 0765.53003)]. Reviewer: Thomas Hasanis (Ioannina) Cited in 1 ReviewCited in 26 Documents MSC: 53A05 Surfaces in Euclidean and related spaces 53A40 Other special differential geometries Keywords:Minkowski space; non-developable ruled surface Citations:Zbl 0765.53003 PDFBibTeX XMLCite \textit{Y. H. Kim} and \textit{D. W. Yoon}, J. Geom. Phys. 49, No. 1, 89--100 (2004; Zbl 1078.53006) Full Text: DOI References: [1] Baikoussis, C.; Koufogiorgos, Th., On the inner curvature of the second fundamental form of helicoidal surfaces, Arch. Math., 68, 169-176 (1997) · Zbl 0870.53004 [2] Blair, D. E.; Koufogiorgos, Th., Ruled surfaces with vanishing second Gaussian curvature, Monatsh. Math., 113, 177-181 (1992) · Zbl 0765.53003 [3] B.-Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, World Scientific, Singapore, 1984.; B.-Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, World Scientific, Singapore, 1984. [4] Chen, B.-Y.; Piccinni, P., Submanifolds with finite type Gauss map, Bull. Aust. Math. Soc., 35, 161-186 (1987) · Zbl 0672.53044 [5] Choi, S. M., On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space, Tsukuba J. Math., 19, 285-304 (1995) · Zbl 0855.53010 [6] Graves, L. K., Codimension one isometric immersions between Lorentz spaces, Trans. Am. Math. Soc., 252, 367-392 (1979) · Zbl 0415.53041 [7] Kim, Y. H.; Yoon, D. W., Ruled surfaces with pointwise 1-type Gauss map, J. Geom. Phys., 34, 191-205 (2000) · Zbl 0962.53034 [8] Kobayashi, O., Maximal surfaces in the 3-dimensional Minkowski space \(L^3\), Tokyo J. Math., 6, 297-309 (1983) · Zbl 0535.53052 [9] Koufogiorgos, Th.; Hasanis, T., A characteristic property of the sphere, Proc. Am. Math. Soc., 67, 303-305 (1977) · Zbl 0379.53030 [10] Koutroufiotis, D., Two characteristic properties of the sphere, Proc. Am. Math. Soc., 44, 176-178 (1974) · Zbl 0283.53002 [11] Kühnel, W., Zur inneren Krümmung der zweiten Grundform, Monatsh. Math., 91, 241-251 (1981) · Zbl 0449.53043 [12] I.V. de Woestijne, Minimal surfaces in the 3-dimensional Minkowski space, in: Geometry and Topology of Submanifolds: II, World Scientific, Singapore, 1990, pp. 344-369.; I.V. de Woestijne, Minimal surfaces in the 3-dimensional Minkowski space, in: Geometry and Topology of Submanifolds: II, World Scientific, Singapore, 1990, pp. 344-369. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.