  A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang
in algebraic dynamics is here established: if $X$ is a projective variety over
an algebraically closed field of characteristic zero which admits a global
algebraic vector field $v:X\to TX$ such that $(X,v)$ has no proper invariant
subvarieties then $X$ is an abelian variety. Vector fields on abelian varieties
with this property are also examined.
