system
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human
Can k (the curvature of spacetime) be complex?

So in our cosmology lectures we've looked at k from a basic "if it's positive, it does this, if it's zero it does that, if it's negative it does this other thing" point-of-view,with the lecturer saying that a full General Relativity treatment of k will be left till the fourth year.  So I'm wondering; can k be complex/imaginary?  Is that a thing which can happen, perhaps when doing the full GR treatment of it?  If so, what would the physical meaning of such a value be?
gpt
The parameter k shows up only in maximally symmetric spaces, but the curvature is always real-valued in GR. General Relativity is basically differencial geometry in a space with a lorentzian metric. The metric only has real-valued entries and thus the Riemannian curvature tensor also is real-valued (it can be constructed from the derivatives of the metric).