Families of flat minimal tori in \(\mathbb{C} P^ n\)
type: Item
instance of: scholarly article
title: Families of flat minimal tori in \(\mathbb{C} P^ n\)
zbMATH Open document ID: 0838.53047
author: Gary R. Jensen
author: Ruijia Liao
published in: Journal of Differential Geometry
publication date: 1996-03-20T00:00:00Z
review text: Infinite families of noncongruent, flat minimal tori are found in \(\mathbb{C} P^n\) for \(n\geq 3\). Continuous families of such tori are found when \(n\geq 5\). These examples are all weakly Lagrangian, but not, in general, contained in a unitary copy of \(\mathbb{R} P^n\subset \mathbb{C} P^n\). Among these minimal tori, some have a cyclic harmonic sequence while others have an infinite noncyclic harmonic sequence. It is shown that for a generic flat torus, there is no isometric, weakly Lagrangian harmonic map from it into \(\mathbb{C} P^n\). Infinite families of noncongruent, flat minimal tori are found in \(S^{2m+ 1}\) for \(m\geq 2\). Continuous families of such tori are found when \(m\geq 3\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 844215
zbMATH Keywords: totally real harmonic maps
zbMATH Keywords: minimal surface
zbMATH Keywords: minimal tori
zbMATH Keywords: harmonic sequence
MaRDI profile type: Publication
Wikidata QID: Q115177990
full work available at URL: https://doi.org/10.4310/jdg/1214457033
OpenAlex ID: W1585411309
DOI: 10.4310/JDG/1214457033
description: scientific article; zbMATH DE number 844215