Minimal Lagrangian submanifolds in \(\mathbb{CP}^n\) with diagonal metric
Generalizing previous work in the two dimensional case [\textit{A Mironov}, ``Finite-gap minimal Lagrangian submanifolds in \(\mathbb{CP}^2\)'', Osaka: Osaka Municipal Universities Press. OCAMI Studies 3, 185--196 (2010; Zbl 1232.53050)], the text provides a construction of Lagrangian mappings \({\mathbb R}^n\to\mathbb{CP}^n\) in terms of Baker-Akhiezer functions, hence in terms of \(\theta\)-functions on a given Riemann surface \(\Gamma\) (Cor. 2). A condition for the constructed Lagrangian mapping to be minimal is formulated in terms of a holomorphic involution on the underlying Riemann surface (Theorem 2) and an explicit example of the construction of a minimal Lagrangian mapping \({\mathbb R}^3\to\mathbb{CP}^3\) is discussed.
scientific article; zbMATH DE number 5897322
scientific article