Periodic cubic Hyperbolic Schrödinger equation on T2

In this paper we consider the cubic Hyperbolic Schrödinger equation (1.1) on torus T2, and get the sharp L4 Strichartz estimate, which implies that (1.1) is analytic locally well-posed in Hs(T2) for s>1/2, meanwhile, the ill-posedness in Hs(T2) for s<1/2 is also obtained.