Abstract
In this paper we investigate (k+1)-dimensional generalized ruled surfaces generated by a one-parameter family of k-dimensional linear subspaces of the n-dimensional Euclidean space En. All generalized ruled hypersurfaces (i. e. (n−1)-dimensional generalized ruled surfaces) with an everywhere vanishing mean curvature are listed. In other words, a complete characterization is given of all minimal ruled hypersurfaces. Moreover the principal curvatures of these surfaces are determined.
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Aumann, G. Die Minimalhypekregelflächen. Manuscripta Math 34, 293–304 (1981). https://doi.org/10.1007/BF01165542
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DOI: https://doi.org/10.1007/BF01165542