Variational Methods in Lorentzian Geometry

Riemannian manifolds Covariant derivative Vector field Morse Index A Fermat principle for stationary Lorentzian manifolds Banach Manifolds A Morse Theory for geodesics on stationary Lorentzian manifolds Conjugate Points Deformation Theorem Complete Riemannian Manifold Globally Hyperbolic Hilbert manifolds Geodesics on splitting manifolds Levi Civita Connection Lorentzian Metric Geometric Index Nondegenerate Critical Point Hilbert Manifold Saddle Point Theorem Smooth Manifold Stationary Lorentzian manifolds Stronger Convexity Assumption Schwarzschild Space Time Timelike Curve Stationary Limit Surface Smooth Functional Timelike Geodesics Lorentzian manifold Riemannian Case Smooth Vector Fields