# Classification results for biharmonic submanifolds in spheres

@article{Balmu2007ClassificationRF, title={Classification results for biharmonic submanifolds in spheres}, author={Adina Balmuş and Stefano Montaldo and Cezar Oniciuc}, journal={Israel Journal of Mathematics}, year={2007}, volume={168}, pages={201-220} }

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…

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