The parameter rigid flows on oriented 3-manifolds

Abstract

A flow defined by a nonsingular smooth vector field $X$ on a closed manifold $M$ is said to be parameter rigid if given any real valued smooth function $f$ on $M$, there are a smooth funcion $g$ and a constant $c$ such that $f=X(g)+c$ holds. We show that the parameter rigid flows on closed orientable 3-manifolds are smoothly conjugate to Kronecker flows on the 3-torus with badly approximable slope.