27 citations · 162 across the 37 of their papers we have counts for
37 papers
Sectional curvature and structure functions of a two-dimensional Lorentzian manifold
A. Z. Ali, Yu. L. Sachkov
In this note we obtain a formula for the sectional curvature on an arbitrary two-dimensional smooth manifold equipped with a Lorentzian metric .
Lorentzian anti-de Sitter plane
A. Z. Ali, Yu. L. Sachkov
In this paper, we study a two-dimensional Lorentzian problem on the anti-de Sitter plane. Using methods of geometric control theory and differential geometry, it was possible to co…
Flat sub-Lorentzian structures on Martinet distribution
Yu. L. Sachkov
Two flat sub-Lorentzian problems on the Martinet distribution are studied. For the first one, the attainable set has a nontrivial intersection with the Martinet plane, but for the…
Sub-Riemannian geodesics on the Heisenberg 3D nil-manifold
A. Glutsyuk, Yu. Sachkov
We study the projection of the left-invariant sub-Riemannian structure on the 3D Heisenberg group to the Heisenberg 3D nil-manifold -- the compact homogeneous space of …
Lorentzian distance on the Lobachevsky plane
Yu. L. Sachkov
Left-invariant Lorentzian structures on the 2D solvable non-Abelian Lie group are studied. Sectional curvature, attainable sets, Lorentzian length maximizers, distance, spheres, an…
Sub-Lorentzian distance and spheres on the Heisenberg group
Yu. L. Sachkov, E. F. Sachkova
The left-invariant sub-Lorentzian problem on the Heisenberg group is considered. An optimal synthesis is constructed, the sub-Lorentzian distance and spheres are described.