In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1...
In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.