Traditional Notation
Among those who use index notation for tensors, it is common to use the letter R to represent three different things:
- the Riemann curvature tensor: or
- the Ricci tensor:
- the scalar curvature: R
These three are then distinguished from each other by their number of indices: the Riemann tensor has four indices, the Ricci tensor has two indices, and the Ricci scalar has zero indices. Those not using an index notation usually reserve R for the full Riemann curvature tensor.
Read more about this topic: Scalar Curvature
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