Parallel mean curvature surfaces in four-dimensional homogeneous spaces
arXiv:1701.03740 · doi:10.24064/iwts2016.2017.8
Abstract
We survey different classification results for surfaces with parallel mean curvature immersed into some Riemannian homogeneous four-manifolds, including real and complex space forms, and product spaces. We provide a common framework for this problem, with special attention to the existence of holomorphic quadratic differentials on such surfaces. The case of spheres with parallel mean curvature is also explained in detail, as well as the state-of-the-art advances in the general problem.
19 pages, 1 table. Minor mistakes have been corrected, and some references have been added in the second and third versions