The Levi-Civita Connection

  • John M. LeeEmail author
Part of the Graduate Texts in Mathematics book series (GTM, volume 176)


On each Riemannian or pseudo-Riemannian manifold, there is a unique connection determined by the metric, called the Levi-Civita connection. After defining it, we investigate the exponential map, which conveniently encodes the collective behavior of geodesics and allows us to study the way they change as the initial point and initial velocity vary.

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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