Abstract: The sub-Riemannian problem on the Heisenberg group is well known, it
> is a cornerstone of sub-Riemannian geometry.
> It can be stated as a time-optimal problem with a planar set of control
> parameters, a circle.
> The talk will be devoted to its natural variation, the time-optimal problem with
> a hyperbola as a set of control parameters.
> This variation is the sub-Lorentzian problem on the Heisenberg group.
>
> For this problem we will describe the following results:
> 1) The reachable set from the identity of the group,
> 2) Pontryagin maximum principle, parameterization of extremal trajectories,
> exponential mapping,
> 3) Diffeomorphic property of the exponential mapping, its inverse,
> 4) Optimality of extremal trajectories, optimal synthesis,
> 5) Sub-Lorentzian distance,
> 6) Sub-Lorentzian spheres of positive and zero radii.
> Results 1), 2) were obtained by M.Grochowski (2006), the rest results are new.
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