# Non-existence of orthogonal complex structures on the round 6-sphere

## TL;DR

This paper reviews the established mathematical fact that the 6-sphere cannot admit an orthogonal complex structure compatible with its standard round metric, highlighting a fundamental geometric limitation.

## Contribution

It provides a concise review of the proof that no orthogonal complex structure exists on the 6-sphere with the round metric.

## Key findings

- No orthogonal complex structure on the 6-sphere exists
- The result is well-known in differential geometry
- The note summarizes key ideas of the proof

## Abstract

In this short note, we review the well-known result that there is no orthogonal complex structure on the 6-sphere with respect to the round metric.