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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 D. E. Blair and T. Koufogiorgos [Monatsh. Math. 113, No. 3, 177–181 (1992; Zbl 0765.53003)].

MSC:

53A05 Surfaces in Euclidean and related spaces
53A40 Other special differential geometries

Citations:

Zbl 0765.53003
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Full Text: DOI

References:

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