Biharmonic homogeneous hypersurfaces in compact symmetric spaces

TL;DR

This paper classifies all biharmonic hypersurfaces in certain symmetric spaces, specifically those arising as orbits of specific group actions, expanding understanding of their geometric properties.

Contribution

It provides a complete classification of biharmonic hypersurfaces in irreducible compact symmetric spaces as orbits of commutative Hermann actions.

Findings

All biharmonic hypersurfaces in the studied spaces are classified.

Biharmonic hypersurfaces correspond to regular orbits of specific group actions.

The work extends known classifications in symmetric space geometry.

Abstract

In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits of commutative Hermann actions of cohomogeneity one.