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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