In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature submanifolds in spheres.
"Properties of Biharmonic Submanifolds in Spheres." J. Geom. Symmetry Phys. 17 87 - 102, 2010. https://doi.org/10.7546/jgsp-17-2010-87-102