Biharmonic hypersurfaces in Riemannian symmetric spaces. I. (Q290931)

The paper under review studies some classifications and constructions of biharmonic hypersurfaces in Riemannian symmetric spaces. An ingredient here is that it focuses on the irreducible compact semi-simple Riemannian symmetric spaces \(G/K\) with the Killing metric which turn it into an Einstein manifold, and in this case, the equation for biharmonic hypersurfaces in an Einstein space obtained in [\textit{Y.-L. Ou}, Pac. J. Math. 248, No. 1, 217--232 (2010; Zbl 1205.53066)] reduced to a single simple equation \(|A|^2=1/2\). The hypersurfaces studied in the paper include those defined by the tubes around some totally geodesic submanifolds and some geodesic spheres of certain radii. The results of the paper add some new examples of biharmonic hypersurfaces in Riemannian symmetric spaces and also help to complete a classification of biharmonic homogeneous hypersurfaces in a compact Riemannian symmetric spaces of rank one.