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  • Print publication year: 2019
  • Online publication date: October 2019

16 - Riemannian Curvature


In this chapter we introduce "Ehresmann connections," with their associated notions of parallel transport and curvature. We then specify these notions in the case of a Riemannian manifold, where one can find a canonical connection associated with the metric structure, called Levi–Civita connection. We then explain how this connection is related to the theory of Jacobi curves developed in the previous chapter.

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