  A classical theorem of H. Hopf asserts that a closed connected smooth
manifold admits a nowhere vanishing vector field if and only if its Euler
characteristic is zero. R. Brown generalized Hopf's result to topological
manifolds, replacing vector fields with path fields. In this note, we give an
equivariant analog of Brown's theorem for locally smooth $G$-manifolds where
$G$ is a finite group.
