Abstract
The Dini helicoid is a surface obtained by a screw motion of the tractrix. In this paper, we consider various analogs of the Dini helicoid in the three-dimensional Minkowski space. As profiles, we take nontrivial pseudo-Euclidean analogs of the tractrix different from pseudo-Euclidean circles. We prove that on analogs of the Dini helicoid in a the pseudo-Euclidean space, one of the following metrics is induced: the metric of the Lobachevsky plane, the metric of the de Sitter plane, or a degenerate metric.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 180, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor V. T. Bazylev. Moscow, April 22-25, 2019. Part 2, 2020.
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Kostin, A.V. On Dini Helicoids in the Minkowski Space. J Math Sci 276, 517–524 (2023). https://doi.org/10.1007/s10958-023-06772-9
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DOI: https://doi.org/10.1007/s10958-023-06772-9