Abstract
In this work, we study the existence of both global smooth and Shatah-Struwe's solutions of the critical wave equation in variable coefficients in dimension d of space
square(A)u + \u\(4/(d-2))u = partial derivative(t)(2)u - div(A(x) . del(x)u) + \u\(4/(d-2))u = 0, R-t X R-x(d),
where A is a regular function valued in the space of d x d positive definite matrix and which is the identity outside a fixed compact.