Non-existence of orthogonal complex structures on 6-sphere with a metric close to the round one

TL;DR

This paper reviews multiple proofs demonstrating that the six-sphere cannot admit an orthogonal complex structure, especially for metrics close to the standard round metric, highlighting the robustness of this non-existence result.

Contribution

The paper generalizes existing proofs to show the non-existence of orthogonal complex structures on the six-sphere for metrics near the round one.

Findings

Orthogonal complex structures do not exist on the 6-sphere with metrics close to the round metric.

Multiple proofs confirm the non-existence, including those by Bor, Hernandez-Lamoneda, Sekigawa, and Vanhecke.

The generalization strengthens the understanding of the geometric constraints on the 6-sphere.

Abstract

I review several proofs for non-existence of orthogonal complex structures on the six-sphere, most notably by G. Bor and L. Hernandez-Lamoneda, but also by K. Sekigawa and L. Vanhecke that we generalize for metrics close to the round one. Invited talk at MAM-1 workshop, 27-30 March 2017, Marburg.