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?

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?