How Do Nearby Geodesics Deviate in Curved Spaces?

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The discussion focuses on the geodesic deviation equation and its mathematical characterization in curved spaces, specifically seeking clarity beyond relativity contexts. The Jacobi geodesic deviation formula is highlighted as a key reference, applicable in Riemannian geometry. It indicates how geodesics from a single point deviate, involving the Riemannian curvature tensor. Participants suggest looking into textbooks that cover this topic for a comprehensive understanding. The conversation emphasizes the importance of the Jacobi formula in understanding geodesic behavior in curved spaces.
ledol83
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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!
 
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That's the Jacobi geodesic deviation formula, which is discussed in many textbooks on Riemannian geometry (the Lorentzian version is almost identical).
 

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