- the left-hand side of the (tensor) Bianchi identity for
a symmetric connection is

where

*K*is the Riemann curvature tensor - expanding in terms of Christoffel symbols of the second kind, one obtains

- this sum contains 72 terms, each of which is a product of 2 or 3
Christoffel symbols, for a total of 180 Christoffel symbols
- however,
upon simplifying this expression by consistently renaming the dummy
indices, the simple result of zero is obtained, which verifies the
identity

Richard Liska