The biharmonic stress-energy tensor and the Gauss map

On the Gauss Map with Vanishing Biharmonic stress-energy tensor

We study the biharmonic stress-energy tensor $S_2$ of Gauss map. Adding few assumptions, the Gauss map with vanishing $S_2$ would be harmonic.

The stress-energy tensor for biharmonic maps

Using Hilbert's criterion, we consider the stress-energy tensor associated to the bienergy functional. We show that it derives from a variational problem on metrics and exhibit the peculiarity of dimension four. First, we use this tensor to construct new examples of biharmonic maps, then classify maps with vanishing or parallel stress-energy tensor and Riemannian immersions whose stress-energy tensor is proportional to the metric.

关于p-双调和子流形与应力p-双能量张量

On the p-biharmonic submanifolds and stress p-bienergy tensors

本文研究空间形式中的p-双调和子流形，给出其充要条件，并揭示应力p-双能量张量的新性质。

Submanifolds with Biharmonic Gauss Map

We generalize the Ruh-Vilms problem by characterizing the submanifolds in Euclidean spaces with proper biharmonic Gauss map and we construct examples of such hypersurfaces.

Biharmonic surfaces of constant mean curvature

We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the Gaussian curvature on pseudo-umbilicity. Finally, the condition of biharmonicity is shown to enable an extension of the classical Hopf theorem to CMC surfaces in any ambient Riemannian manifold.

Four dimensional biharmonic hypersurfaces in nonzero space form have constant mean curvature

In this paper, through making careful analysis of Gauss and Codazzi equations, we prove that four dimensional biharmonic hypersurfaces in nonzero space form have constant mean curvature. Our result gives the positive answer to the conjecture proposed by Balmus-Montaldo-Oniciuc in 2008 for four dimensional hypersurfaces.