Isometric deformations of pseudoholomorphic curves in the nearly K{\"a}hler sphere $\mathbb{S}^6$

TL;DR

This paper studies the rigidity and deformability of pseudoholomorphic curves in the nearly Kähler sphere S^6, describing their moduli space and establishing a Schur type theorem for minimal surfaces in spheres.

Contribution

It characterizes the moduli space of isometric minimal surfaces in S^6 that are pseudoholomorphic, and proves a Schur type theorem for minimal surfaces in spheres.

Findings

Description of the moduli space of pseudoholomorphic minimal surfaces in S^6

Rigidity and deformability results for these surfaces

A Schur type theorem for minimal surfaces in spheres

Abstract

The aim of the paper is to investigate the rigidity and the deformability of pseudoholomorphic curves in the nearly K{\"a}hler sphere $\mathbb{S}^6,$ among minimal surfaces in spheres. Under various assumptions we describe the moduli space of all noncongruent minimal surfaces $f\colon M\to\mathbb{S}^n$ that are isometric to a pseudoholomorphic curve in $\mathbb{S}^6.$ Moreover, we prove a Schur type theorem (see \cite[p. 36]{Chnew}) for minimal surfaces in spheres.