Classification results for biharmonic submanifolds in spheres |
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Authors: | A. Balmus S. Montaldo C. Oniciuc |
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Affiliation: | (1) Dipartimento di Matematica, Università degli Studi di Cagliari, Via Ospedale 72, 09124 Cagliari, Italia;(2) Faculty of Mathematics, “Al.I. Cuza” University of Iasi, Bd. Carol I Nr. 11, 700506 Iasi, Romania |
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Abstract: | 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) the conformally flat biharmonic hypersurfaces. We obtain some rigidity results for pseudoumbilical 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 The first author was supported by a INdAM doctoral fellowship, Italy. The second author was supported by PRIN 2005, Italy. The third author was supported by Grant CEEX ET 5871/2006, Romania |
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