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

ber70
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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.
 
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Minkowski spacetime is a semi-riemannian spacetime that is flat. Curved semi-riemannian spacetimes include the Schwarzschild spacetime, and the FRW spacetime with matter.
 
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