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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)].

##### MSC:
 53A05 Surfaces in Euclidean space 53A40 Other special differential geometries
##### Keywords:
Minkowski space; non-developable ruled surface
Full Text:
##### References:
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