The aim of this paper is to prove that there exists no cohomogeneity one G-invariant proper biharmonic hypersurface into the Euclidean space ℝn, where G denotes a transformation group which acts on ℝn 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.

On cohomogeneity one biharmonic hypersurfaces into the Euclidean space

MONTALDO, STEFANO;RATTO, ANDREA
2016

Abstract

The aim of this paper is to prove that there exists no cohomogeneity one G-invariant proper biharmonic hypersurface into the Euclidean space ℝn, where G denotes a transformation group which acts on ℝn 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.
Biharmonic immersions; Biharmonic maps; Cohomogeneity one hypersurfaces; Equivariant differential geometry; Transformation groups; Mathematical physics; Physics and astronomy (all); Geometry and topology
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/176219
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