  In this paper, using the structures of cone and bicone fields on vector
bundles, the author introduces a ILB (inverse limit of
  Banach)- manifold structure on $\mathcal M$ the space of
  Riemannian metrics on a noncompact manifold $M$. In the last section, it is
proven that, this way, on the open submanifold $\mathcal{M}_{finite}$ of finite
volume metrics, the canonical Riemannian metric is defined.
