  A model of two--dimensional gravity with an action depending only on a linear
connection is considered. This model is a topological one, in the sense that
the classical action does not contain a metric or zweibein at all. A metric and
an additional vector field are instead introduced in the process of solving
equations of motion for the connection. They satisfy the constant curvature
equation. It is shown that the general solution of these equations of motion
can be described by using the space of orbits under the action of the Weyl
group in the functional space containing all pairs formed by a metric and a
vectorfield. It is shown also that this model admits an equivalent description
by using a family of actions depending on the metric and the connection as
independent variables.
