Geodesic
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

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

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. 
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     author = {A. V. Kostin},
     title = {Beltrami theorem in {Minkowski} space},
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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/