Does anyone have a good book or reference on computing riemannian connections. I'm looking at Do Carmo and can't find any examples. For ex. If X = y(d/dx) + x(d/dy) + w(d/dz) -z(d/dw), Y = z(d/dx) - w(d/dy) - x(d/dz) + y(d/dw), Z = w(d/dx) + z(d/dy) - y(d/dz) - x(d/dw) being the classical frame field on s3. How would I go about computing nabla_X(X), nabla_X(Y), nabla_X(Z) in terms of X,Y,Z where nabla is the levi civita connection. I would like to see one example if possible, or something similar. Thanks.