Minimal Lagrangian submanifolds in \(\mathbb{CP}^n\) with diagonal metric
type: Item
instance of: scholarly article
title: Minimal Lagrangian submanifolds in \(\mathbb{CP}^n\) with diagonal metric
zbMATH Open document ID: 1232.53068
DOI: 10.1134/S0037446606010113
author: I. P. Rybnikov
published in: Siberian Mathematical Journal
publication date: 2011-05-19T00:00:00Z
review text: 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.
reviewed by: Udo Hertrich-Jeromin
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 5897322
zbMATH Keywords: Lagrangian submanifold
zbMATH Keywords: minimal submanifold
zbMATH Keywords: Baker-Akhiezer function
zbMATH Keywords: spectral curve
zbMATH Keywords: Riemann surface
MaRDI profile type: Publication
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full work available at URL: s0037446606010113
OpenAlex ID: W1999023380
description: scientific article; zbMATH DE number 5897322