Cayley structures on $S^6$ as a twistor bundle sections

TL;DR

This paper investigates nearly Kähler structures on the 6-sphere via twistor bundle sections, revealing a family of such structures passing through any given point and exploring their properties.

Contribution

It introduces a one-parameter family of twistor bundle sections that generate nearly Kähler structures on the 6-sphere, expanding understanding of their geometric configurations.

Findings

Existence of a 1-parameter family of sections passing through any point

These sections produce nearly Kähler structures on the sphere

Properties of the sections are characterized

Abstract

The nearly K\"{a}hler structures on the 6-sphere, as a twistor bundle sections are researched. We show that for any point of twistor bundle there exists an 1-parametric family of sections, passing through the point, which give nearly K\"{a}hler structures on the round sphere. Some properties of those sections are found.