Trajectories under a Vectorial Potential on Stationary Manifolds
نویسنده
چکیده
By using variational methods, we study the existence and multiplicity of trajec-tories under a vectorial potential on (standard) stationary Lorentzian manifolds possibly with boundary. 1. Introduction and statement of the results. The pair (ᏸ,g) is called Lorentzian manifold if ᏸ is a connected finite-dimensional smooth manifold with dim ᏸ ≥ 2 and g is a Lorentzian metric on ᏸ, that is, g is a smooth symmetric two covariant tensor field such that for any z ∈ ᏸ, the bilinear form g(z)[·, ·] induced on T z ᏸ is nondegenerate and of index ν(g) = 1. Its points are called events. A Lorentzian manifold (ᏸ,g) is called (standard) stationary if ᏸ is a product manifold
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