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 Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k?1 in even-dimensional pseudo-Euclidean space Es2k, Ms?12k?1 in even-dimensional de Sitter space Ss2kcc0, and Ms2k?1 in even-dimensional anti-de Sitter space ?s2kcc0 are minimal.