Minimal Lagrangian submanifolds in \(\mathbb{C}\mathbb{P}^3\) and the sinh-Gordon equation (Q5954149)

The authors study 3-dimensional minimal Lagrangian submanifolds of a 3-dimensional complex projective space \(\mathbb{P}_3\) which admit a unit length Killing vector field whose integral curves are geodesics. They prove that such submanifolds can be obtained from either horizontal holomorphic curves in \(\mathbb{P}_3\) or solutions of the 2-dimensional sinh-Gordon equation.