Elliptic Weingarten hypersurfaces of Riemannian products

Abstract Let be either a simply connected space form or rank‐one symmetric of the noncompact type. We consider Weingarten hypersurfaces , which are those whose principal curvatures and angle function satisfy relation being W differentiable is with respect to . When on positive cone strictly convex hypersurface determined by said elliptic show that, for certain class functions there exist rotational topological spheres entire graphs over M establish Jellett–Liebmann‐type theorem showing that compact, embedded sphere. Other uniqueness results complete these ambient spaces obtained. also obtain existence constant scalar curvature invariant translations (parabolic hyperbolic). apply our methods give new proofs main Manfio Tojeiro classification sectional