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- Flat_manifold abstract "In mathematics, a Riemannian manifold is said to be flat if its curvature is everywhere zero. Intuitively, a flat manifold is one that "locally looks like" Euclidean space in terms of distances and angles, e.g. the interior angles of a triangle add up to 180°.The universal cover of a complete flat manifold is Euclidean space. This can be used to prove the theorem of Bieberbach (1911, 1912) that all compact flat manifolds are finitely covered by tori; the 3-dimensional case was proved earlier by Schoenflies (1891).".
- Flat_manifold wikiPageID "12756616".
- Flat_manifold wikiPageLength "2893".
- Flat_manifold wikiPageOutDegree "21".
- Flat_manifold wikiPageRevisionID "651104124".
- Flat_manifold wikiPageWikiLink Affine_manifold.
- Flat_manifold wikiPageWikiLink Category:Riemannian_manifolds.
- Flat_manifold wikiPageWikiLink Clifford_torus.
- Flat_manifold wikiPageWikiLink Compact_space.
- Flat_manifold wikiPageWikiLink Complete_metric_space.
- Flat_manifold wikiPageWikiLink Complete_space.
- Flat_manifold wikiPageWikiLink Conformally_flat_manifold.
- Flat_manifold wikiPageWikiLink Covering_space.
- Flat_manifold wikiPageWikiLink Crystallographic_group.
- Flat_manifold wikiPageWikiLink Curvature.
- Flat_manifold wikiPageWikiLink Euclidean_space.
- Flat_manifold wikiPageWikiLink Klein_bottle.
- Flat_manifold wikiPageWikiLink Mathematics.
- Flat_manifold wikiPageWikiLink Moebius_band.
- Flat_manifold wikiPageWikiLink Möbius_strip.
- Flat_manifold wikiPageWikiLink Nash_embedding_theorem.
- Flat_manifold wikiPageWikiLink Orbifold.
- Flat_manifold wikiPageWikiLink Ricci-flat_manifold.
- Flat_manifold wikiPageWikiLink Riemannian_manifold.
- Flat_manifold wikiPageWikiLink Seifert_fiber_space.
- Flat_manifold wikiPageWikiLink Space_form.
- Flat_manifold wikiPageWikiLink Space_group.
- Flat_manifold wikiPageWikiLink Torus.
- Flat_manifold wikiPageWikiLink Universal_cover.
- Flat_manifold wikiPageWikiLink Wallpaper_group.
- Flat_manifold wikiPageWikiLink Wallpaper_groups.
- Flat_manifold wikiPageWikiLinkText "Flat manifold".
- Flat_manifold wikiPageWikiLinkText "flat Riemannian metric".
- Flat_manifold wikiPageWikiLinkText "flat manifold".
- Flat_manifold wikiPageWikiLinkText "flat".
- Flat_manifold wikiPageWikiLinkText "plane".
- Flat_manifold authorlink "Ernest Vinberg".
- Flat_manifold first "E.B.".
- Flat_manifold hasPhotoCollection Flat_manifold.
- Flat_manifold id "c/c027190".
- Flat_manifold last "Vinberg".
- Flat_manifold title "Crystallographic group".
- Flat_manifold title "Flat Manifold".
- Flat_manifold urlname "FlatManifold".
- Flat_manifold wikiPageUsesTemplate Template:Citation.
- Flat_manifold wikiPageUsesTemplate Template:Eom.
- Flat_manifold wikiPageUsesTemplate Template:Harvs.
- Flat_manifold wikiPageUsesTemplate Template:Harvtxt.
- Flat_manifold wikiPageUsesTemplate Template:MathWorld.
- Flat_manifold subject Category:Riemannian_manifolds.
- Flat_manifold comment "In mathematics, a Riemannian manifold is said to be flat if its curvature is everywhere zero. Intuitively, a flat manifold is one that "locally looks like" Euclidean space in terms of distances and angles, e.g. the interior angles of a triangle add up to 180°.The universal cover of a complete flat manifold is Euclidean space.".
- Flat_manifold label "Flat manifold".
- Flat_manifold sameAs Flache_Mannigfaltigkeit.
- Flat_manifold sameAs Variété_plate.
- Flat_manifold sameAs Varietà_piatta.
- Flat_manifold sameAs m.02x3hrm.
- Flat_manifold sameAs Q601110.
- Flat_manifold sameAs Q601110.
- Flat_manifold wasDerivedFrom Flat_manifold?oldid=651104124.
- Flat_manifold isPrimaryTopicOf Flat_manifold.