Mean curvature of hypersurfaces in Killing submersions with bounded shadow

Abstract

Given a complete hypersurface isometrically immersed in an ambient manifold, in this paper we provide a lower bound for the norm of the mean curvature vector field of the immersion assuming that: 1)The ambient manifold admits a Killing submersion with unit‐length Killing vector field. 2)The projection of the image of the immersion is bounded in the base manifold. 3)The hypersurface is stochastically complete, or the immersion is proper.