Christoffel symbols, LeviCivita connection
The LeviCivita connection involves the Christoffel (1,2)tensor field, which is implemented by the command ΜΓ. Assume our metric is that of the geometrical , parametrized in spherical coordinates as
Then, the Christoffel (1,2)tensor field is
Choosing slightly different coordinates results in
The LeviCivita connection is equivalent to a special covariant derivative, which we implement by Μ▽ in a brief way.

The command Μ▽ determines the covariant derivative of tensor fields of arbitrary rank. Below, we compute the covariant derivative of the vector field {,,}. The result is a (1,1)tensor field.
Created by Mathematica (December 22, 2006) 