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Trajectories under a vectorial potential on stationary manifolds. (English) Zbl 1028.58014

The author studies the existence and multiplicity of trajectories on a Lorentzian manifold for a problem generalizing the one of geodesic connectedness.
The approach is variational relying on critical point theory.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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