  The linearized massive gravity in three dimensions, over any maximally
symmetric background, is known to be presented in a self-dual form as a first
order equation which encodes not only the massive Klein-Gordon type field
equation but also the supplementary transverse-traceless conditions. We
generalize this construction to higher dimensions. The appropriate dual
description in d dimensions, additionally to a (non-symmetric) tensor field
$h_{\mu\nu}$, involves an extra rank-(d-1) field equivalently represented by
the torsion rank-3 tensor. The symmetry condition for $h_{\mu\nu}$ arises
on-shell as a consequence of the field equations. The action principle of the
dual theory is formulated. The focus has been made on four dimensions. Solving
one of the fields in terms of the other and putting back in the action one
obtains two other equivalent formulations of the theory in which the action is
quadratic in derivatives. In one of these representations the theory is
formulated entirely in terms of a rank-2 non-symmetric tensor $h_{\mu\nu}$.
This quadratic theory is not identical to the Fierz-Pauli theory and contains
the coupling between the symmetric and antisymmetric parts of $h_{\mu\nu}$.
Nevertheless, the only singularity in the propagator is the same as in the
Fierz-Pauli theory so that only the massive spin-2 particle is propagating. In
the other representation, the theory is formulated in terms of the torsion
rank-3 tensor only. We analyze the conditions which follow from the field
equations and show that they restrict to 5 degrees of freedom thus producing an
alternative description to the massive spin-2 particle. A generalization to
higher dimensions is suggested.
