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We propose a general notion of parallel transport on RCD spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space.
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Nicola Gigli, Enrico Pasqualetto, On the notion of parallel transport on RCD spaces. Rev. Mat. Iberoam. 36 (2020), no. 2, pp. 571–609DOI 10.4171/RMI/1140