Gravity in the Riemannian Universe

I noticed that Greg Egan doesn't seem to talk about how Gravity would work in the Riemannian Universe. For Galilean Relativity there is Newtons Law of Gravity and for Lorentzian Relativity there is the General theory of Relativity. How would Gravity work differently in the Riemannian Universe from how it works in our Universe?

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Gravity in the Riemannian Universe

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