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Constructions of Type \(III^+\) helicoidal surfaces in Minkowski space with desity. (English) Zbl 1419.53024

Summary: In this paper, we construct a helicoidal surface of type \(III^+\) with prescribed weighted mean curvature and weighted Gaussian curvature in the Minkowski \(3\)-space \(R^3_1\) with a positive density function. We get a result for minimal case. Also we give examples of helicoidal surface with prescribed weighted mean curvature and Gaussian curvature.

MSC:

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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References:

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