Variational Methods in Lorentzian Geometry - 9780367449438

CRC Press

This book focuses on the applications of variational methods and critical point theory on infinite dimensional manifolds, to some problems in Lorentzian Geometry which have a variational nature, such as existence and multiplicity results on geodesics. > Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold. > 1. Semiriemannian manifolds 2. Hilbert manifolds 3. Stationary Lorentzian manifolds 4. Stationary Lorentzian manifolds with convex boundary 5. A Morse Theory for geodesies on stationary Lorentzian manifolds 6. A Fermat principle for stationary Lorentzian manifolds 7. Applications 8. Geodesics on splitting manifolds