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Submanifolds of ${E}^{m}$ with harmonic mean curvature vector. (English) Zbl 0778.53046
Author’s abstract: “We study isometric immersions of Riemannian manifolds into a Euclidean space with harmonic mean curvature vector, also known as biharmonic immersions. While it is still an open question whether such immersions exist (other than minimal ones) we prove some nonexistence results, e.g. in the cases of submanifolds with constant mean curvature, pseudoumbilical submanifolds $\left(dim\ne 4\right)$, or hypersurfaces with at most two distinct principal curvatures”.
##### MSC:
 53C42 Immersions (differential geometry)
##### Keywords:
minimal immersions; biharmonic immersion