  We derive a manifestly duality-symmetric formulation of the action principle
for conformal gravity linearized around Minkowski space-time. The analysis is
performed in the Hamiltonian formulation, the fourth-order character of the
equations of motion requiring the formal treatment of the three-dimensional
metric perturbation and the extrinsic curvature as independent dynamical
variables. The constraints are solved in terms of two symmetric potentials that
are interpreted as a dual three-dimensional metric and a dual extrinsic
curvature. The action principle can be written in terms of these four dynamical
variables, duality acting as simultaneous rotations in the respective spaces
spanned by the three-dimensional metrics and the extrinsic curvatures. A
twisted self-duality formulation of the equations of motion is also provided.
