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- Bergers_sphere abstract "In Riemannian geometry, a Berger sphere, named after Marcel Berger, is a standard 3-sphere with Riemannian metric from a one-parameter family, which can be obtained from the standard metric by shrinking along fibers of a Hopf fibration. It is interesting in that it is one of the simplest examples of Gromov collapse.More precisely, one first considers the Lie algebra spanned by generators x1, x2, x3 with Lie bracket [xi,xj] = −2εijkxk. This is well known to correspond to the simply connected Lie group S3. Then, taking the product S3×R, extending the Lie bracket so that the generator x4 is left invariant under the operation of the Lie group, and taking the quotient by αx1+βx4, where α2+β2 = 1, we finally obtain the Berger spheres B(β).There are also higher-dimensional analogues of Berger spheres.".
- Bergers_sphere wikiPageID "11205365".
- Bergers_sphere wikiPageLength "2075".
- Bergers_sphere wikiPageOutDegree "8".
- Bergers_sphere wikiPageRevisionID "607100501".
- Bergers_sphere wikiPageWikiLink Category:Riemannian_geometry.
- Bergers_sphere wikiPageWikiLink Category:Spheres.
- Bergers_sphere wikiPageWikiLink Collapsing_manifold.
- Bergers_sphere wikiPageWikiLink Hopf_fibration.
- Bergers_sphere wikiPageWikiLink Lie_algebra.
- Bergers_sphere wikiPageWikiLink Marcel_Berger.
- Bergers_sphere wikiPageWikiLink Riemannian_geometry.
- Bergers_sphere wikiPageWikiLinkText "Berger's sphere".
- Bergers_sphere wikiPageUsesTemplate Template:Differential-geometry-stub.
- Bergers_sphere wikiPageUsesTemplate Template:Reflist.
- Bergers_sphere subject Category:Riemannian_geometry.
- Bergers_sphere subject Category:Spheres.
- Bergers_sphere hypernym Sphere.
- Bergers_sphere type ArtificialSatellite.
- Bergers_sphere comment "In Riemannian geometry, a Berger sphere, named after Marcel Berger, is a standard 3-sphere with Riemannian metric from a one-parameter family, which can be obtained from the standard metric by shrinking along fibers of a Hopf fibration. It is interesting in that it is one of the simplest examples of Gromov collapse.More precisely, one first considers the Lie algebra spanned by generators x1, x2, x3 with Lie bracket [xi,xj] = −2εijkxk.".
- Bergers_sphere label "Berger's sphere".
- Bergers_sphere sameAs Q4447641.
- Bergers_sphere sameAs m.02r3m6h.
- Bergers_sphere sameAs Сферы_Берже.
- Bergers_sphere sameAs Q4447641.
- Bergers_sphere wasDerivedFrom Bergers_sphere?oldid=607100501.
- Bergers_sphere isPrimaryTopicOf Bergers_sphere.