Killing vector fields and Lagrangian submanifolds of the nearly Kaehler S6

AbstractIn this paper, we study Lagrangian submanifolds of the nearly Kähler 6-sphere S6(1). We obtain a classification of the Lagrangian submanifolds which admit a unit length Killing vector field whose integral curves are great circles by relating them to almost complex surfaces in S6(1) or holomorphic curves in CP2(4)