  We prove a Koszul formula for the Levi-Civita connection for any
pseudo-Riemannian bilinear metric on a class of centered bimodule of
noncommutative one-forms. As an application to the Koszul formula, we show that
our Levi-Civita connection is a bimodule connection. We construct a spectral
triple on a fuzzy sphere and compute the scalar curvature for the Levi-Civita
connection associated to a canonical metric.
