  We systematically develop the metric aspects of nonassociative differential
geometry tailored to the parabolic phase space model of constant locally
non-geometric closed string vacua, and use it to construct preliminary steps
towards a nonassociative theory of gravity on spacetime. We obtain explicit
expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection
in nonassociative Riemannian geometry on phase space, and write down Einstein
field equations. We apply this formalism to construct R-flux corrections to the
Ricci tensor on spacetime, and comment on the potential implications of these
structures in non-geometric string theory and double field theory.
