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On rational isotropic congruences of lines

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Abstract.

The aim of this paper is to show a way to find an explicit parametrization of rational isotropic congruences of lines in Euclidean three-space \(\mathbb{R}^{3} .\) It will be shown that also the focal surfaces of these congruences admit a rational parametrization. Furthermore, the close relation of isotropic congruences of lines to minimal surfaces will be used to find the related polynomial minimal surfaces.

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  1. Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10, 1040, Wien, Österreich

    Boris Odehnal

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  1. Boris Odehnal
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Correspondence to Boris Odehnal.

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Odehnal, B. On rational isotropic congruences of lines. J. geom. 81, 126–138 (2004). https://doi.org/10.1007/s00022-004-1739-0

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  • DOI: https://doi.org/10.1007/s00022-004-1739-0

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