# Anti-de Sitter space Minkowski space is the maximally symmetric solution to Einstein's equation without the cosmological constant. With a negative cosmological constant, the maximally symmetric space is anti-de Sitter (AdS). In Euclidean signature, AdS is just the hyperbolic space $H_n$, and the metric can be written as$ds^2_{H_n}=L^2(d\rho^2+\sinh^2\rho \,d\Omega^2_{n-1}).$It is easy to verify that it has constant negative curvature $-n(n-1)/L^2$.