An ILB- Manifold Structure on the Set of Riemannian Metrics on a Noncompact Manifold

Details An ILB- Manifold Structure on the Set of Riemannian Metrics on a Noncompact Manifold An ILB- Manifold Structure on the Set of Riemannian Metrics on a Noncompact Manifold

2004-02-17

arxiv.org/abs/math/0402280v1

Mathematics

Differential Geometry

8 pages

Scientific paper

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.

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