Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability
In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold endowed with a weight function and having a closed conformal Killing vector field with conformal factor , that is, graphs constructed through the flow generated by and which are defined over an integral leaf of the foliation orthogonal to . For such graphs, we establish some rigidity results under appropriate constraints on the -mean curvature. Afterwards, we obtain some stability results...