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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Parallel transport with minimum length curve
I would know if it is possible to create a natural parallel transport on a Riemannian manifold $M$ with the following procedure.
Define a minimum length curve (m.l.c.) $\gamma$ from $P$ to $Q$ requir …