Hypersurfaces in hyperbolic space associated with the conformal scalar curvature equation Δu+kun+2n−2=0

We consider a class of oriented hypersurfaces in hyperbolic space satisfying ∑r=0n(c−n+2r)(nr)Hr=0, where HrHr is the rth mean curvature and c   is a real constant. We show how this class is characterized by a harmonic map derived from the two hyperbolic Gauss maps. By looking at hypersurfaces as orthogonal to a congruence of geodesics, we also show the relation of such hypersurfaces with solutions of the equation Δu+kun+2n−2=0, where k∈{−1,0,1}k∈{−1,0,1}. Finally, we apply the relation mentioned above to obtain examples and geometrical results for the hypersurfaces.