Polyharmonic hypersurfaces into complex space forms

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 ${\mathbb{CP}}^n$ and ${\mathbb{CH}}^n$, respectively. Moreover, we study the stability of biharmonic hypersurfaces and compute the normal index for a large family of solutions.

16 pages, 0 figures. v2: new references, Corollary 5.3 has been improved, and some minor changes. v3: improved exposition

References in corpus (4)

• Polyharmonic hypersurfaces into pseudo-Riemannian space forms
• Polyharmonic surfaces in $3$-dimensional homogeneous spaces
• Explicit harmonic self-maps of complex projective spaces
• On the second variation of the biharmonic Clifford torus in S^4