We verify the 3-dimensional Glassey conjecture on asymptotically flat manifolds (R^1+3, g), where the metric g is certain small space-time perturbation of the flat metric, as well as the nontrapping asymptotically Euclidean manifolds. Moreover, for radial asymptotically flat manifolds (R^1+n, g) with n> 3, we verify the Glassey conjecture in the radial case. High dimensional wave equations with higher regularity are also discussed. The main idea is to exploit local energy and KSS estimates with

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... variable coefficients, together with the weighted Sobolev estimates including trace estimates.