# What is the curvature of an empty universe?

My calculations tell me an empty universe has hyperbolic curvature. Is this correct? If it is, can anyone help me understand why this is intuitively?

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What do you mean by empty? Whether you mean no matter and/or no dark matter and/or no dark energy density makes a difference. –  Michael Brown Apr 23 '13 at 13:17
I mean completely empty $\rho_M=\rho_R=\rho_{\Lambda}=0$. –  misi Apr 24 '13 at 2:53

Right. So $k=-1$ is what my calculations give me. So what you (and the article) are saying is that although the space is hyperbolic, the Riemann scalar is $0$. Is this right? So the space is hyperbolic but the space time as a whole is flat? –  misi Apr 24 '13 at 2:49