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Results tagged with lie-groups
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user 142151
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
1
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Small deformations of maximally symmetric 3-spaces
I am looking for all 'small' deformations of the three 3-dimensional Riemannian spaces with maximal symmetry, the pseudo-sphere, Eucidean space and the sphere. By a theorem by Fubini (1903) the deform …
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Small deformations of maximally symmetric 3-spaces
No there are no others.
Bianchi shows in ``Sugli spazi a tre dimensioni che ammettono un gruppo continuo di movimenti,'' Memorie di Matematica e di Fisica della Societa Italiana delle Scienze 11 (189 …
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Deformations of the 4-sphere with 8-dimensional isometry groups
I am looking for deformations of the 4-sphere with 8-dimensional isometry group, like a 4-dimensional Berger sphere.
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answer
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A pseudo-Riemannian version of a theorem by Fubini
Guido Fubini, ``Sugli spazii che ammettono un gruppo continuo di movimenti,'' Annali di Mat., ser. 3, 8 (1903) 54.: Let $M$ be a Riemannian manifold of dimension $d\ge 3$. Its isometry group cannot be …
- 427
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A pseudo-Riemannian version of a theorem by Fubini
I just found the answer by G. S. Hall (2003) in Class. Quantum Grav. 20 3745.
Theorem 8. Let $M$ be a connected smooth paracompact manifold of dimension $n ≥ 3$ admitting a smooth metric $g$ of signat …
- 427
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3-dimensional Riemannian manifolds with 4-dimensional isometry group
Is there a list of all 3-dimensional, connected Riemannian manifolds with 4-dimensional isometry group?
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0
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Maximal symmetry at the speed of light
Are there examples of 1 + 3 dimensional pseudo-Riemannian manifolds with 6 dimensional isometry group whose orbits are light-like (i.e., the metric restricted to each orbit is degenerate)?
Here is a …
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