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.
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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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Balmus, A., Montaldo, S. & Oniciuc, C. Classification results for biharmonic submanifolds in spheres. Isr. J. Math. 168, 201–220 (2008). https://doi.org/10.1007/s11856-008-1064-4
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DOI: https://doi.org/10.1007/s11856-008-1064-4