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

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