Lagrangian surfaces in the complex hyperquadric Q2Q2

In this paper, we introduce a one-form ΦΦ associated to a Lagrangian immersion ff from Riemann surface MM into the complex hyperquadric Q2Q2. It is proved that ff is minimal if and only if ΦΦ is vanishing and ff is H-minimal if and only if ΦΦ is holomorphic. As an application, a family of S1S1-equivariant minimal Lagrangian tori in Q2Q2 are obtained.