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

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.