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Results tagged with riemannian-geometry
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user 142151
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
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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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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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On sub-maximally symmetric Riemannian spaces
Is there a 4-dimensional Riemannian manifold with 8-dimensional isometry group?
Context: Guido Fubini (Annali di Mat., ser. 3, 8 (1903) 54) shows that the dimension $n$ of the isometry group of a $d$- …
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