Classification of Bianchi
The classification of Bianchi is a classification of the real algebras of Dregs of Dimension 3, given by Luigi Bianchi.
Classification of Bianchi
Interest for cosmology
In Cosmology, this classification is used for the homogeneous Espace-temps of dimension 3+1. The Univers of Friedmann-Lemaître-Robertson-Walker is isotropic, which is a particular case of type I described above (the general case corresponds to homogeneous universe, but whose expansion is anisotropic, i.e. from which the Rate growth is different along three orthogonal directions (see Métrique of Kasner). Type IX of the classification of Bianchi reveals a particularly complex dynamics of the expansion, this one being done by the succession of times of the anisotropic expansion type (with two directions expanding, one in contraction) which are separated by periods when the growth rates in the three directions change in a brutal and relatively chaotic way.
References
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See, chapter 7.2, pages 168 to 179.
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