43 citations
2 papers
math.DG2011★ 43 cited
Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries
Ye-Lin Ou, Ze-Ping Wang
We prove that a totally umbilical biharmonic surface in any -dimensional Riemannian manifold has constant mean curvature. We use this to show that a totally umbilical surface in…
math.DG2010★ 36 cited
Biharmonic Riemannian submersions from 3-manifolds
Ze-Ping Wang, Ye-Lin Ou
An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a surface into 3-dimensional Eucl…