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Lagrangian surfaces in the complex hyperquadric Q2

Institution:	1. School of Mathematics Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, China;2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui province, China;3. Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, Anhui, China

Abstract:	In this paper, we introduce a one-form $Φ$ associated to a Lagrangian immersion $f$ from Riemann surface $M$ into the complex hyperquadric $Q_{2}$ . It is proved that $f$ is minimal if and only if $Φ$ is vanishing and $f$ is H-minimal if and only if $Φ$ is holomorphic. As an application, a family of $S^{1}$ -equivariant minimal Lagrangian tori in $Q_{2}$ are obtained.

Keywords:	Lagrangian surface Minimal surface Holomorphic one-form
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