Abstract
In this paper we study real hypersurfaces in the nearly Kaehler 6-sphere
S
6
and show that there are three almost contact metric structures on a real hypersurface. Then we use a conformal vector field on the 6-sphere
S
6
and study its influence on the almost contact metric structures on the real hypersurface
M
and use it to characterize the hyperspheres in
S
6
.