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Normal trajectories in stationary spacetimes under the action of an external field with quadrant asymptotic behavior. (English) Zbl 1171.53333

Summary: The aim of this note is to study the existence of normal trajectories joining two given submanifolds under the action of an external field in a standard stationary space-time. Here, it is assumed that both the growth of the potential and that of the coefficients of the metric are critical in a suitable sense.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C22 Geodesics in global differential geometry
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
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