Cayley Structures on S 6 as Sections if Twistor Bundle

We consider nearly Kähler structures on a 6-dimensional sphere as sections of the twistor bundle over the sphere and prove that for any point of the space of twistor bundle there is a one-parameter family of nearly Kähler structures passing through the point. We study some properties of such one-parameter families. © 2017, Springer Science+Business Media New York.