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Does Newton's law of universal gravitation depend on the geometry of the manifold? For example, what happens to formulas if we take the projective plane as our universe? How can one model "the mass" on the projective plane or on torus?

I am a math grad with very elementary physics knowledge. I know almost all mathematical objects used in the physics but don't know how you use or apply them. So, I need a book on these topics. Any recommendations?

Thanks.