  Given a geodesic line $\gamma$ the hyperbolic space $\mathbb H^n$ we
formulate a necessary and sufficient condition for a function along this
geodesic which measure the mean curvature of totally umbilical leaves of a
foliation orthogonal to $\gamma$. Then we extend the result to $\gamma$ being a
hypercycle i.e. a geodesic on a hypersurface equidistant from the totally
geodesic one.
