On Dini helicoids in the Minkowski space
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 2, Tome 180 (2020), pp. 50-57
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The Dini helicoid is a surface obtained by 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 the degenerate metric.
Keywords:
Lobachevsky plane, de Sitter plane, Dini helicoid.
@article{INTO_2020_180_a6,
author = {A. V. Kostin},
title = {On {Dini} helicoids in the {Minkowski} space},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {50--57},
publisher = {mathdoc},
volume = {180},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2020_180_a6/}
}
A. V. Kostin. On Dini helicoids in the Minkowski space. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 2, Tome 180 (2020), pp. 50-57. http://geodesic.mathdoc.fr/item/INTO_2020_180_a6/