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- What is the difference between spacetime curvature and curvature index of space?

The presence of the cosmological constant produces a flat spacetime universe with Ω = 1. There is also the curvature index of space k, which can be +1, 0, -1. But it is possible to have any of these values of k with Λ > 0 or Λ < 0. How is the curvature of spacetime determined by Λ different from that of the curvature index of space k?