On p-Parabolicity of Riemannian Submersions

We provide some criteria to $p$-parabolicity of Riemannian submersions. In particular, if $N$ is $p$-parabolic and $\pi:M\to N$ is a Riemannian submersion with uniformly bounded volume of fibers, then $M$ is also $p$-parabolic. In the case of warped manifolds we characterize $p$-parabolicity in terms of a volume growth condition.