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Probably the intuition should be that curvature is the commutator of infinitesimal parallel transports, so it is antisymmetric for the same reason asthat the Lie bracket is.

Probably the intuition should be that curvature is the commutator of infinitesimal parallel transports, so it is antisymmetric for the same reason as the Lie bracket is.

Probably the intuition should be that curvature is the commutator of infinitesimal parallel transports, so it is antisymmetric for the same reason that the Lie bracket is.

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Probably the intuition should be that curvature is the commutator of infinitesimal parallel transports, so it is antisymmetric for the same reason thatas the Lie bracket is.

Probably the intuition should be that curvature is the commutator of infinitesimal parallel transports, so it is antisymmetric for the same reason that the Lie bracket is.

Probably the intuition should be that curvature is the commutator of infinitesimal parallel transports, so it is antisymmetric for the same reason as the Lie bracket is.

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Probably the intuition should be that curvature is the commutator of infinitesimal parallel transports, so it is antisymmetric for the same reason that the Lie bracket is.