An existence and multiplicity result for periodic trajectories on stationary Lorentzian manifolds, possibly with boundary, whose proof is based on a Morse theory approach is presented. A Lorentzian manifold is a smooth connected finite-dimensional manifold M equipped with a (0,2) tensor field g such that for any z∈M g(z) [·,·] is a nondegenerate symmetric bilinear form on the tangent space TzM having exactly one negative eigenvalue. Moreover, relativistic spacetimes are a particular class of Lorentzian manifolds of dimension four
Periodic trajectories on stationary Lorentzian manifolds / Bartolo, R. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 43:7(2001), pp. 883-903. [10.1016/S0362-546X(99)00246-1]
Periodic trajectories on stationary Lorentzian manifolds
Bartolo R
2001-01-01
Abstract
An existence and multiplicity result for periodic trajectories on stationary Lorentzian manifolds, possibly with boundary, whose proof is based on a Morse theory approach is presented. A Lorentzian manifold is a smooth connected finite-dimensional manifold M equipped with a (0,2) tensor field g such that for any z∈M g(z) [·,·] is a nondegenerate symmetric bilinear form on the tangent space TzM having exactly one negative eigenvalue. Moreover, relativistic spacetimes are a particular class of Lorentzian manifolds of dimension fourI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
