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

Famous quotes containing the word traditional:

    “Americans want action for their money. They are fascinated by its self-reproducing qualities if it’s put to work.... Gold-hoarding goes against the American grain; it fits in better with European pessimism than with America’s traditional optimism.”
    —Paula Nelson (b. 1945)