  We consider the quadratically semilinear wave equation on R^d, d>=3, equipped
with a Riemannian metric. This metric is non-trapping and approaches the
Euclidean metric polynomially at infinity. Using Mourre estimates and the Kato
theory of smoothness, we obtain a Keel-Smith-Sogge type inequality for the
linear equation. Thanks to this estimate, we prove long time existence (d=3)
and global existence (d>3) for the nonlinear problem with small initial data.
