Weak Solutions to Stochastic Wave Equations with Values in Riemannian Manifolds

Let M be a compact Riemannian manifold. We prove existence of a global weak solution of the stochastic wave equation D(t)u(t) = D(x)u(x) + (X-u + lambda(0)(u)u(t) + lambda(1)(u)u(x)) (W) over dot. where X is a continuous vector field on M, lambda(0) and lambda(1) are continuous vector bundles homomorphisms from TM to TM, and W is a spatially homogeneous Wiener process on R with finite spectral measure. We use recently introduced general method of constructing weak solutions of SPDEs that does not rely on any martingale representation theorem.