Biharmonic hypersurfaces in Riemannian symmetric spaces I

Abstract

We classify biharmonic geodesic spheres in the Cayley projective plane. Our results completes the classification of all biharmonic homogeneous hypersurfaces in simply connected compact Riemannian symmetric spaces of rank 1. In addition we show that complex Grassmannian manifolds, and exceptional Lie groups $F_4$ and $G_2$ admit proper biharmonic real hypersurfaces.