Pseudoholomorphic curves on nearly Kahler manifolds

TL;DR

This paper proves the compactness of the moduli space of pseudoholomorphic curves on nearly Kahler manifolds, providing tools to analyze such curves on specific 6-dimensional spheres with special structures.

Contribution

It establishes the compactness of the moduli space of pseudoholomorphic curves on nearly Kahler manifolds, a key step for further geometric analysis.

Findings

Connected components of the moduli space are compact.

Application to pseudoholomorphic curves on the 6-sphere with G_2-invariant structure.

Framework for studying pseudoholomorphic curves in nearly Kahler geometry.

Abstract

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of pseudoholomorphic curves on M is compact. This can be used to study pseudoholomorphic curves on a 6-dimensional sphere with the standard (G_2-invariant) almost complex structure.