  We consider Schr\"odinger equation with a non-degenerate metric on the
Euclidean space. We study local in time Strichartz estimates for the
Schr\"odinger equation without loss of derivatives including the endpoint case.
In contrast to the Riemannian metric case, we need the additional assumptions
for the well-posedness of our Schr\"odinger equation and for proving Strichartz
estimates without loss.
