Unit Killing Vector Fields on Nearly Kahler Manifolds
  We study 6-dimensional nearly Kahler manifolds admitting a Killing vector field of unit length. In the compact case it is shown that up to a finite cover there is only one geometry possible, that of the 3--symmetric space $S^3 \times S^3$. 
Andrei Moroianu, Paul-Andi Nagy, Uwe Semmelmann