The Lorentzian Problem on the Group $SU(2)$
We consider a left-invariant Lorentzian problem on SU(2). The following questions are addressed: complete controllability, existence of length maximizers, extremals, curvature.
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arXiv subjects
A. Z. Ali
Publications and source records attributed to A. Z. Ali.
Sectional Curvature and Structural Functions of a Two-Dimensional or Three-Dimensional Lorentzian Manifold
We derive a formula for the sectional curvature on an arbitrary two-dimensional or three-dimensional smooth manifold equipped with a Lorentzian metric.
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Sectional curvature and structure functions of a two-dimensional Lorentzian manifold
In this note we obtain a formula for the sectional curvature on an arbitrary two-dimensional smooth manifold $M$ equipped with a Lorentzian metric $g$.
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Lorentzian anti-de Sitter plane
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 construct an orthonormal frame, calculate extremal trajectories, describe the reachable set, construct an optimal synthesis, and describe the Lorentzian distance.
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