Barbosa, J. M.; Dajczer, M.; Jorge, L. P. Minimal ruled submanifolds in spaces of constant curvature. (English) Zbl 0544.53044 Indiana Univ. Math. J. 33, 531-547 (1984). Let \(\bar M\) be a standard space of constant curvature, and A:\({\mathbb{R}}\to ISO(\bar M)\) a one-parameter group of isometries. Let \(S\subset \bar M\) be totally geodesic and orthogonal to the A-orbits. Then X:\({\mathbb{R}}\times S\to \bar M\), (s,p)\(\mapsto A(s)p\) is called a generalized helicoid. Main result: Every minimal ruled submanifold of \(\bar M\) is part of generalized helicoid. Reviewer: D.Ferus Cited in 1 ReviewCited in 27 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53B25 Local submanifolds Keywords:constant curvature; group of isometries; totally geodesic; generalized helicoid; minimal ruled submanifold PDFBibTeX XMLCite \textit{J. M. Barbosa} et al., Indiana Univ. Math. J. 33, 531--547 (1984; Zbl 0544.53044) Full Text: DOI