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math.DG2025
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 .
math.DG2024
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 …
math.DG2024
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…