What is the different between Minkowski Space an Semi Riemann Space?

[ber70]

Last summer I took Semi Riemann Geometry lesson. Almost all the definitions in Semi Riemann geometry are with the same Minkowski geometry. I don't understand what is the different between Minkowski Space an Semi Riemann Space.

[atyy]

Minkowski spacetime is a semi-riemannian spacetime that is flat. Curved semi-riemannian spacetimes include the Schwarzschild spacetime, and the FRW spacetime with matter.