Biharmonic constant mean curvature surfaces in Killing submersions

Abstract

A $3$-dimensional Riemannian manifold is called Killing submersion if it admits a Riemannian submersion over a surface such that its fibers are the trajectories of a complete unit Killing vector field. In this paper, we give a characterization of proper biharmonic CMC surfaces in a Killing submersion. In the last part, we also classify the proper biharmonic Hopf cylinders in a Killing submersion.

14 pages

References in corpus (1)

• On the classification of Killing submersions and their isometries