On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space
The author classifies spacelike and timelike ruled surfaces in 3-dimensional Minkowski spacetime \(\mathbb{R}^3_1\) whose Gauss map \(\xi\) satisfies \(\Delta \xi= A\xi\) for some \(3\times 3\) real matrix \(A\), where \(\Delta\) is the Laplacian of the surfaces. He proves that such surfaces are locally either \(\mathbb{R}^2_1\), \(S^1_1\times \mathbb{R}^1\), \(\mathbb{R}^1_1\times S^1\), \(\mathbb{R}^2\) or \(H^1\times \mathbb{R}^1\). Ruled surfaces in a Euclidean 3-space satisfying \(\Delta\xi= A\xi\) were classified by \textit{C. Baikoussis} and \textit{D. E. Blair} in [Glasgow Math. J. 34, No. 3, 355-359 (1992; Zbl 0762.53004)]. Ruled surfaces of finite type in a Euclidean \(n\)-space in general were completely classified by \textit{C. Baikoussis}, the reviewer and \textit{L. Verstraelen} in [Tokyo J. Math. 16, No. 2, 341-349 (1993; Zbl 0798.53055)].
scientific article; zbMATH DE number 895938