Spaces of Riemannian metrics on open manifolds (Q1895237)
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scientific article; zbMATH DE number 785215
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spaces of Riemannian metrics on open manifolds |
scientific article; zbMATH DE number 785215 |
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Spaces of Riemannian metrics on open manifolds (English)
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15 August 1995
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Let \(M\) be an open manifold. On certain subspaces of the set of all Riemannian metrics on \(M\) (metrics of bounded geometry and \(C^m\) or \(L^r_2\)-regularity) suitable topologies are defined. In the \(L^r_2\)-case the components of such a space are Hilbert manifolds. Their infinite-dimensional geometry is studied. In particular, it is shown that their sectional curvature is non-positive.
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open-manifolds
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bounded geometry
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spaces of Riemannian metrics
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sectional curvature
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