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We prove a microlocal smoothing effect of Schr\"odinger equations onmanifolds. We employ radially homogeneous wavefront sets introduced by Ito andNakamura (Amer. J. Math., 2009). In terms of radially homogeneous wavefrontsets, we can apply our theory to both of asymptotically conical and hyperbolicmanifolds. We relate wavefront sets in initial states to radially homogeneouswavefront sets in states after a time development. We also prove a relationbetween radially homogeneous wavefront sets and homogeneous wavefront sets andprove a special case of Nakamura (2005).

Propagation of singularities under Schr\"odinger equations on manifolds with ends