  We study the quantum Riemannian geometry of quantum projective spaces of any
dimension. In particular we compute the Riemann and Ricci tensors, using
previously introduced quantum metrics and quantum Levi-Civita connections. We
show that the Riemann tensor is a bimodule map and derive various consequences
of this fact. We prove that the Ricci tensor is proportional to the quantum
metric, giving a quantum analogue of the Einstein condition, and compute the
corresponding scalar curvature. Along the way we also prove several results for
various objects related to those mentioned here.
