On Dini Helicoids in the Minkowski Space

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 pr...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 276; no. 4; pp. 517 - 524
Main Author Kostin, A. V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2023
Springer
Springer Nature B.V
Subjects
Analogs
Euclidean geometry
Mathematics
Mathematics and Statistics
Minkowski space
53B30
Lobachevsky plane
Dini helicoid
de Sitter plane
53A35
Online AccessGet full text
ISSN1072-3374
1573-8795
DOI10.1007/s10958-023-06772-9

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Summary: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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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06772-9