Bianchi Classification - Curvature of Bianchi Spaces

Curvature of Bianchi Spaces

The Bianchi spaces have the property that their Ricci tensors can be separated into a product of the basis vectors associated with the space and a coordinate-independent tensor.

For a given metric

(where

are 1-forms), the Ricci curvature tensor is given by:

where the indices on the structure constants are raised and lowered with which is not a function of .

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