Abstract
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.
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Lee, J.M. (2018). The Levi-Civita Connection. In: Introduction to Riemannian Manifolds. Graduate Texts in Mathematics, vol 176. Springer, Cham. https://doi.org/10.1007/978-3-319-91755-9_5
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DOI: https://doi.org/10.1007/978-3-319-91755-9_5
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-91755-9
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