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- Preissmans_theorem abstract "In Riemannian geometry, a field of mathematics, Preissman's theorem is a statement that restricts the possible topology of a negatively curved compact Riemannian manifold M. Specifically, the theorem states that every non-trivial abelian subgroup of the fundamental group of M must be isomorphic to the additive group of integers, Z.For instance, a compact surface of genus two admits a Riemannian metric of curvature equal to −1 (see the uniformization theorem). The fundamental group of such a surface is isomorphic to the free group on two letters. Indeed, the only abelian subgroups of this group are isomorphic to Z.A corollary of Preissman's theorem is that the n-dimensional torus, where n is at least two, admits no Riemannian metric of negative sectional curvature.".
- Preissmans_theorem wikiPageID "33848514".
- Preissmans_theorem wikiPageLength "1603".
- Preissmans_theorem wikiPageOutDegree "14".
- Preissmans_theorem wikiPageRevisionID "607983530".
- Preissmans_theorem wikiPageWikiLink Abelian_group.
- Preissmans_theorem wikiPageWikiLink Abelian_subgroup.
- Preissmans_theorem wikiPageWikiLink Category:Theorems_in_Riemannian_geometry.
- Preissmans_theorem wikiPageWikiLink Compact_space.
- Preissmans_theorem wikiPageWikiLink Fundamental_group.
- Preissmans_theorem wikiPageWikiLink Genus_(mathematics).
- Preissmans_theorem wikiPageWikiLink Integer.
- Preissmans_theorem wikiPageWikiLink Integers.
- Preissmans_theorem wikiPageWikiLink Isomorphic.
- Preissmans_theorem wikiPageWikiLink Isomorphism.
- Preissmans_theorem wikiPageWikiLink Mathematics.
- Preissmans_theorem wikiPageWikiLink Riemannian_geometry.
- Preissmans_theorem wikiPageWikiLink Riemannian_manifold.
- Preissmans_theorem wikiPageWikiLink Sectional_curvature.
- Preissmans_theorem wikiPageWikiLink Topology.
- Preissmans_theorem wikiPageWikiLink Torus.
- Preissmans_theorem wikiPageWikiLink Uniformization_theorem.
- Preissmans_theorem wikiPageWikiLinkText "Preissman's theorem".
- Preissmans_theorem hasPhotoCollection Preissmans_theorem.
- Preissmans_theorem wikiPageUsesTemplate Template:Geometry-stub.
- Preissmans_theorem wikiPageUsesTemplate Template:Reflist.
- Preissmans_theorem subject Category:Theorems_in_Riemannian_geometry.
- Preissmans_theorem hypernym Statement.
- Preissmans_theorem comment "In Riemannian geometry, a field of mathematics, Preissman's theorem is a statement that restricts the possible topology of a negatively curved compact Riemannian manifold M. Specifically, the theorem states that every non-trivial abelian subgroup of the fundamental group of M must be isomorphic to the additive group of integers, Z.For instance, a compact surface of genus two admits a Riemannian metric of curvature equal to −1 (see the uniformization theorem).".
- Preissmans_theorem label "Preissman's theorem".
- Preissmans_theorem sameAs m.0hnb5t0.
- Preissmans_theorem sameAs Q7240001.
- Preissmans_theorem sameAs Q7240001.
- Preissmans_theorem wasDerivedFrom Preissmans_theoremoldid=607983530.
- Preissmans_theorem isPrimaryTopicOf Preissmans_theorem.