Locally symmetric minimal affine Lagrangian surfaces in \(\mathbb{C}^{2}\) (Q1014279)

In the Riemannian theory of minimal Lagrangian submanifolds, it is known (in the positive definite case) that a minimal Lagrangian submanifolds of \(\mathbb C^n\) of constant sectional curvature must be flat. This fact was proved by \textit{N. Ejiri} [Proc. Am. Math. Soc. 84, 243--246 (1982; Zbl 0485.53022)]. The affine version of the theory of minimal Lagrangian submanifolds also was studied by the author [\textit{B. Opozda}, Geom. Dedicata 121, 155--166 (2006; Zbl 1114.53016)]. In this very interesting paper, the author gives a local classification of locally symmetric minimal affine Lagrangian surfaces in \(\mathbb C^2\).