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Minimal ruled submanifolds associated with Gauss map. (English) Zbl 1400.53015

Summary: We set up the new models of product manifolds, namely a generalized circular cylinder and a generalized hyperbolic cylinder as cylindrical types of ruled submanifold in Minkowski space. We also establish some characterizations of generalized circular cylinders and hyperbolic cylinders in Minkowski space with the Gauss map. We also show that there do not exist non-cylindrical marginally trapped ruled submanifolds with the pointwise 1-type Gauss map of the first kind, which gives a characterization of non-cylindrical minimal ruled submanifolds in Minkowski space.

MSC:

53A35 Non-Euclidean differential geometry
53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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References:

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