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Normal forms for sub-Lorentzian metrics supported on Engel type distributions

We construct normal forms for Lorentzian metrics on Engel distributions under the assumption that abnormal curves are timelike future directed Hamiltonian geodesics. Then we indicate some cases in which the abnormal timelike future directed curve initiating at the origin is geometrically optimal. We also give certain estimates for reachable sets from a point.

preprint2013arXivOpen access
Marek Grochowski
math.DG
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Marek Grochowski

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