Classification results for biharmonic submanifolds in spheres

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We classify biharmonic submanifolds with certain geometric properties in Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces with at most two distinct principal curvatures and the conformally flat biharmonic hypersurfaces. We obtain some rigidity results for pseudo-umbilical biharmonic submanifolds of codimension 2 and for biharmonic surfaces with parallel mean curvature vector field. We also study the type, in the sense of B-Y. Chen, of compact proper biharmonic submanifolds with constant mean curvature in spheres.
Dedicated to Professor Vasile Oproiu on his 65th birthday, 14 pages

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Differential Geometry, 58E20

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http://salesiana.dossiersoluciones.com/handle/123456789/121235

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701155
 http://arxiv.org/abs/math/0701155

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arXiv