Cezar Oniciuc

Biharmonic submanifolds in spheres

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.

BIHARMONIC SUBMANIFOLDS OF S 3

We explicitly classify the nonharmonic biharmonic submanifolds of the unit three-dimensional sphere

On the biharmonic and harmonic indices of the Hopf map

{\mathbb S}^3

The index of biharmonic maps in spheres

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Explicit formulas for biharmonic submanifolds in non-Euclidean 3-spheres

Biharmonic maps are the critical points of the bienergy functional and, from this point of view, generalize harmonic maps. We consider the Hopf map and modify it into a nonharmonic biharmonic map . We show to be unstable and estimate its biharmonic index and nullity. Resolving the spectrum of the vertical Laplacian associated to the Hopf map, we recover Urakawas determination of its harmonic index and nullity.

Biharmonic surfaces of constant mean curvature

Biharmonic maps are the critical points of the bienergy functional and generalise harmonic maps. We investigate the index of a class of biharmonic maps derived from minimal Riemannian immersions into spheres. This study is motivated by three families of examples: the totally geodesic inclusion of spheres, the Veronese map and the Clifford torus.

On cohomogeneity one biharmonic hypersurfaces into the Euclidean space

We obtain the parametric equations of all biharmonic Legendre curves and Hopf cylinders in the 3-dimensional unit sphere endowed with the modified Sasakian structure defined byTanno.

Submanifolds with biharmonic Gauss map

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 inuence 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.

Global Properties of Biconservative Surfaces in

Abstract The aim of this paper is to prove that there exists no cohomogeneity one G -invariant proper biharmonic hypersurface into the Euclidean space R n , where G denotes a transformation group which acts on R n by isometries, with codimension two principal orbits. This result may be considered in the context of the Chen conjecture, since this family of hypersurfaces includes examples with up to seven distinct principal curvatures. The paper uses the methods of equivariant differential geometry. In particular, the technique of proof provides a unified treatment for all these G -actions.

\mathbb{R}^3

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.