Scalar Curvature - Traditional Notation

Traditional Notation

Among those who use index notation for tensors, it is common to use the letter R to represent three different things:

  1. the Riemann curvature tensor: or
  2. the Ricci tensor:
  3. 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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