# Parallel transport on non-collapsed $\mathsf{RCD}(K,N)$ spaces

@article{Caputo2021ParallelTO, title={Parallel transport on non-collapsed \$\mathsf\{RCD\}(K,N)\$ spaces}, author={Emanuele Caputo and Nicola Gigli and Enrico Pasqualetto}, journal={arXiv: Differential Geometry}, year={2021} }

We provide a general theory for parallel transport on non-collapsed ${\sf RCD}$ spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of curves obtained via the flow of sufficiently regular time dependent vector fields: the price that we pay for this generality is that we cannot study parallel transport along a single such curve, but only along almost all of these (in a sense related to the notions of Sobolev vector calculus and… Expand

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