We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in [16], [8], [6], [7]. We then apply the equation to show that the generalized Chen’s conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-p...

We consider in dimension four weakly convergent sequences of approximate biharmonic maps into sphere with bi-tension fields bounded in L for some p > 1. We prove an energy identity that accounts for the loss of Hessian energies by the sum of Hessian energies over finitely many nontrivial biharmonic maps on R.

In this article we prove the regularity of weakly biharmonic maps of domains in Euclidean four space into spheres, as well as the corresponding partial regularity result of stationary biharmonic maps of higher-dimensional domains into spheres. c © 1999 John Wiley & Sons, Inc. Introduction In this article we consider the notion of biharmonic maps and begin an analytic study of the regularity pro...

This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.

In this paper, the reduction of biharmonic map equation in terms of the Maurer-Cartan form for all smooth map of an arbitrary compact Riemannian manifold into a compact Lie group (G, h) with bi-invariant Riemannian metric h is obtained. By this formula, all biharmonic curves into compaqct Lie groups are determined, and all the biharmonic maps of an open domain of R with the conformal metric of ...