Partial Integrability of Almost Complex Structures on Thurston Manifolds

TL;DR

This paper proves that certain symplectic almost complex structures on Thurston manifolds are necessarily of holomorphic type 1, revealing constraints on their integrability.

Contribution

It establishes a partial integrability result for left-invariant symplectic almost complex structures on Thurston manifolds.

Findings

Any compatible structure has holomorphic type 1

Constraints on integrability of almost complex structures

Focus on left-invariant structures on Thurston manifolds

Abstract

We prove that any left-invariant symplectic almost complex structure on a Thurston manifold which is compatible with its canonical left-invariant Riemannian metric has holomorphic type 1.