  We apply geometric tools to study dynamics of two- and threepeakon solutions
of the Camassa--Holm equation. New proofs of asymptotic behavior of the
solutions are given. In particular we recover well-known collision conditions.
Additionally the Gauss curvature (in the twopeakon case) and the sectional
curvature (in the treepeakon case) of corresponding manifolds are computed.
