  We consider least energy solutions to the nonlinear equation $-\Delta_g
u=f(r,u)$ posed on a class of Riemannian models $(M,g)$ of dimension $n\ge 2$
which include the classical hyperbolic space $\mathbb H^n$ as well as manifolds
with unbounded sectional geometry. Partial symmetry and existence of least
energy solutions is proved for quite general nonlinearities $f(r,u)$, where $r$
denotes the geodesic distance from the pole of $M$.
