On $${\varvec{p}}$$ p -Parabolicity of Riemannian Submersions

Abstract

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