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- Berger's_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.".
- Berger's_sphere wikiPageID "11205365".
- Berger's_sphere wikiPageRevisionID "603813785".
- Berger's_sphere hasPhotoCollection Berger's_sphere.
- Berger's_sphere subject Category:Riemannian_geometry.
- Berger's_sphere subject Category:Spheres.
- Berger's_sphere type Abstraction100002137.
- Berger's_sphere type Attribute100024264.
- Berger's_sphere type Environment113934596.
- Berger's_sphere type Situation113927383.
- Berger's_sphere type Sphere114514039.
- Berger's_sphere type Spheres.
- Berger's_sphere type State100024720.
- Berger's_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.".
- Berger's_sphere label "Berger's sphere".
- Berger's_sphere label "Сферы Берже".
- Berger's_sphere sameAs m.02r3m6h.
- Berger's_sphere sameAs Q4447641.
- Berger's_sphere sameAs Q4447641.
- Berger's_sphere sameAs Berger's_sphere.
- Berger's_sphere wasDerivedFrom Berger's_sphere?oldid=603813785.
- Berger's_sphere isPrimaryTopicOf Berger's_sphere.