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 .
Read more about this topic: Bianchi Classification
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“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
—Blaise Pascal (1623–1662)