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
Famous quotes containing the word spaces:
“We should read history as little critically as we consider the landscape, and be more interested by the atmospheric tints and various lights and shades which the intervening spaces create than by its groundwork and composition.”
—Henry David Thoreau (18171862)