Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. V. Kostin
TI  - On Dini helicoids in the Minkowski space
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 50
EP  - 57
VL  - 180
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_180_a6/
LA  - ru
ID  - INTO_2020_180_a6
ER  - 
%0 Journal Article
%A A. V. Kostin
%T On Dini helicoids in the Minkowski space
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 50-57
%V 180
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_180_a6/
%G ru
%F 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/