Biharmonic hypersurfaces in a product space Lm×R

In this paper, we study biharmonic hypersurfaces in a product Lm×R of an Einstein space Lm and a real line R. We prove that a biharmonic hypersurface with constant mean curvature in such a product is either minimal or a vertical cylinder generalizing a result of [36] and [17]. We derived the biharmonic equation for hypersurfaces in Sm×R and Hm×R in terms of the angle function of the hypersurface, and use it to obtain some classifications of biharmonic hypersurfaces in such spaces. These include classifications of biharmonic hypersurfaces which are totally umbilical or semi‐parallel for m≥3, and some classifications of biharmonic surfaces in S2×R and H2×R which are constant angle or belong to certain classes of rotation surfaces.