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Minimal ruled submanifolds in spaces of constant curvature. (English) Zbl 0544.53044

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

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
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