On η-biharmonic hypersurfaces in pseudo-Riemannian space forms

On η-biharmonic hypersurfaces in pseudo-Riemannian space forms

L Du, J Ren – Mathematica Slovaca, 2022

In this paper, η-biharmonic hypersurfaces with constant scalar curvature in 5-dimensional pseudo-Riemannian space forms are studied. We prove that such hypersurfaces with diagonalizable shape operator have constant mean curvature, which gives an affirmative partial answer to the conjecture in [Arvanitoyeorgos, A.— Kaimakamis, FG: Hypersurfaces of type M 2 3 in E 2 4 with proper mean curvature
vector, J. Geom. Phys. 63 (2013), 99–106]. As a result, we give several partial …