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We firstly prove Strichartz estimates for the fractional Schr\"odingerequations on $\mathbb{R}^d$ endowed with a smooth bounded metric $g$. We thenprove Strichartz estimates for the fractional Schr\"odinger and wave equationson compact Riemannian manifolds without boundary $(M,g)$. We finally giveapplications of Strichartz estimates for the local well-posedness of the purepower-type nonlinear fractional Schr\"odinger and wave equations posed on$(M,g)$.

Strichartz estimates for the fractional Schr\"odinger and wave equations on compact manifolds without boundary