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Ruled Weingarten surfaces in Minkowski 3-space

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Abstract:

We characterize all ruled surfaces in Minkowski 3-space with a relation between the Gauss and mean curvature (Weingarten surfaces). It turns out that, except if the rulings are in a null direction, these are given by Lorentzian screw motions of straight lines. However, if the rulings are always in a null direction, then every ruled surface is Weingarten.

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Authors and Affiliations

  1. Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium. e-mail: Franki.Dillen@wis.kuleuven.ac.be¶Senior Research Assistant of National Fund for Scientific Research (Belgium), , , , , , BE

    Franki Dillen

  2. Mathematisches Institut B, Universität Stuttgart, D-70550 Stuttgart, Germany. e-mail: kuehnel@mathematik.uni-stuttgart.de, , , , , , DE

    Wolfgang Kühnel

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  1. Franki Dillen
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  2. Wolfgang Kühnel
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Received: 9 February 1998 / Revised version: 20 December 1998

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Dillen, F., Kühnel, W. Ruled Weingarten surfaces in Minkowski 3-space. manuscripta math. 98, 307–320 (1999). https://doi.org/10.1007/s002290050142

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  • DOI: https://doi.org/10.1007/s002290050142

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