Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures. (1st August 2020) - Yang, Chao; Liu, Jiancheng
Abstract : In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form N s n + 1 c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces M r 2 k − 1 in even-dimensional pseudo-Euclidean space E s 2 k, M s − 1 2 k − 1 in even-dimensional de Sitter space S s 2 k c c > 0, and M s 2 k − 1 in even-dimensional anti-de Sitter space ℍ s 2 k c c < 0 are minimal.