Complete normality conditions for the dynamical systems on Riemannian   manifolds
  New additional equations for the Newtonian dynamical systems on Riemannian manifolds are found. They supplement the previously found weak normality conditions up to the complete normality conditions for Newtonian dynamical systems. 
A.Yu. Boldin, A.A. Bronnikov, V.V. Dmitrieva, R.A. Sharipov (Bashkir   State University, Ufa, Russia)