It can be shown, that the curvature tensor measure the deviation between \(Z\) and its parallel transport along the boundary of an infinitesimal small rectangle spanned by \(X\) and \(Y\) [1, Theorem 7.11].

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• curvature tensor
• parallel transport

References Link to heading

1. J. Lee, Introduction to Riemannian Manifolds. Cham: Springer International Publishing, 2018. doi:10.1007/978-3-319-91755-9