Limit cycles of linear vector fields on (

It is well known that linear vector fields defined in $\mathbb{R}^n$ can not have limit cycles, but this the case for other manifolds. We study existence of cycles bifurcating from a continuum periodic orbits on manifolds form $(\mathbb{S}^2)^m \times \mathbb{R}^n$ when such are perturbed inside class all fields. The done using averaging theory. also present an open problem concerning maximum number \mathbb{R}^n$.