Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures

摘要

In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form with constant sectional curvature and index have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces in even-dimensional pseudo-Euclidean space , in even-dimensional de Sitter space , and in even-dimensional anti-de Sitter space are minimal.