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We explicitly classify the nonharmonic biharmonic submanifolds of the unit three-dimensional sphere ${\mathbb S}^3$.

We give some methods to construct examples of nonharmonic biharmonic submanifolds of the unitn-dimensional sphereSn. In the case of curves inSn we solve explicitly the biharmonic equation.

We study biharmonic submanifolds of the Euclidean sphere that satisfy certain geometric properties. We classify: (i) the biharmonic hypersurfaces with at most two distinct principal curvatures; (ii)… (More)

We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of… (More)

points of the bienergy functional E2(’) = 1 R M j?(’)j 2 vg; where ?(’) is the tension fleld of ’. Biharmonic maps are a natural expansion of harmonic maps (?(’) = 0). Although E2 has been on the… (More)

is linear, thusany harmonic map is biharmonic. We call proper biharmonic the non-harmonicbiharmonic maps.In this paper we shall focus our attention on biharmonic submanifolds, i.e. onsubmanifolds… (More)

We study subelliptic biharmonic maps, i.e., smooth maps ϕ:M→N from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of the energy functional… (More)

In this article we characterize all biharmonic curves of the Cartan-Vranceanu 3-dimensional spaces and we give their explicit parametrizations.

In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.