Characterizations of minimal hypersurfaces immersed in certain warped products

Abstract

Our purpose in this paper is to investigate when a complete two-sided hypersurface immersed with constant mean curvature in a Killing warped product Mn ×ρ R, whose Riemannian base Mn has sectional curvature bounded from below and such that the warping function ρ ∈ C∞ (M ) is supposed to be concave, is minimal (and, in particular, totally geodesic) in the ambient space. Our approach is based on the application of the well known generalized maximum principle of Omori-Yau.

Keywords

• Killing warped product
• constant mean curvature hypersurfaces
• minimal hypersurfaces
• totally geodesic hypersurfaces