4 papers
Sectional Curvature and Structural Functions of a Two-Dimensional or Three-Dimensional Lorentzian Manifold
A. Z. Ali, Yu. L. Sachkov
We derive a formula for the sectional curvature on an arbitrary two-dimensional or three-dimensional smooth manifold equipped with a Lorentzian metric.
The Lorentzian Problem on the Group
A. Z. Ali, Yu. L. Sachkov
We consider a left-invariant Lorentzian problem on SU(2). The following questions are addressed: complete controllability, existence of length maximizers, extremals, curvature.
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…