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Abstract We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for CPⁿ C P n and CHⁿ C H n, respectively. Moreover, we study the stability of biharmonic hypersurfaces and compute the normal index for a large family of solutions.
José Miguel Balado-Alves (Sat,) studied this question.