Difference between the Jacobi equation and geodesic deviation equation

[serali]

http://en.wikipedia.org/wiki/Jacobi_field

also see http://iopscience.iop.org/0305-4470/14/9/029/?ejredirect=.iopscience

What's the difference between the jacobi equation and the geodesic deviation equation?

 

[Reb]

They are the same notion under a different name: The Euler-Lagrange equations for the variation of geodesic length, over the space of geodesics with fixed ends.