Beltrami theorem in Minkowski space
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 73-80
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E. Beltrami proved a theorem on the relationship of curvatures for families of surfaces of revolution in the three-dimensional Euclidean space, which implies that if some surface of revolution $M'$ orthogonally intersects all surfaces obtained from a surface of constant curvature $M$ by translations along the rotation axis, then the curvature of the surface $M'$ is also constant and differs from the curvature of the surface $M$ only in sign. In this paper, we obtain analogs of this theorem for surfaces of revolution in the three-dimensional Minkowski space.
Keywords:
Minkowski space, surface of revolution, Lobachevsky plane, de Sitter plane, space of constant curvature, pseudosphere.
@article{INTO_2022_215_a7,
author = {A. V. Kostin},
title = {Beltrami theorem in {Minkowski} space},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {73--80},
publisher = {mathdoc},
volume = {215},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2022_215_a7/}
}
A. V. Kostin. Beltrami theorem in Minkowski space. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 73-80. http://geodesic.mathdoc.fr/item/INTO_2022_215_a7/