How Do Nearby Geodesics Deviate in Curved Spaces?

[ledol83]

Hi...does anyone have a good description (or a link to it) on geodesic deviation equation?Most of the references i have are in a setting of relativity, which make me all at sea.

Please help me if you know a mathematical characterization of how geodesics from one point deviate (which just involves the Riemannian curvature tensor).

Thanks a bunch!

 

[Chris Hillman]

That's the Jacobi geodesic deviation formula, which is discussed in many textbooks on Riemannian geometry (the Lorentzian version is almost identical).