The Riemann Curvature Tensor is a tensor in Riemannian Geometry that describes the curvature of a manifold. Specifically, it measures the failure (known as the holonomy) of the ability of parallel transport to retain the direction of a vector in a space. In other words, it can be calculated as:
IdentitiesEdit this section
The definition of the Riemann Curvature Tensor immediately implies that:
Now, below are some other identities:
See  .
First Bianchi Identity  .
Second Bianchi Identity  .