On the Woldram Mathworld site, tgs Jacobi tensor is defined to be:

$J^m_{ijk} :=1/2( R^m_{ijk} + R^m_{kji})$

Where $R^m_{ijk}$ is the Riemann curvature tensor.

I've not been able to find anything else about this tensor online. What is it useful for and what has Jacobi to do with it?