Lorentzian manifold
pseudo-Riemannian manifold of signature (1,n)
anti-de Sitter space
maximally symmetric Lorentzian manifold with negative cosmological constant, which appears in the AdS/CFT correspondence
timelike simply connected manifold
Lorentzian manifold that does not contain a closed timelike curve
de Sitter space
maximally symmetric Lorentzian manifold with positive cosmological constant