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Classification of ruled surfaces in Minkowski 3-spaces. (English) Zbl 1078.53006
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 {\it D. E. Blair} and {\it T. Koufogiorgos} [Monatsh. Math. 113, No. 3, 177--181 (1992; Zbl 0765.53003)].

53A05Surfaces in Euclidean space
53A40Other special differential geometries
Full Text: DOI
[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. · Zbl 0537.53049
[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 L3. 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.