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Forums
Physics
Special and General Relativity
Lie derivative and Riemann tensor
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[QUOTE="Orodruin, post: 6169936, member: 510075"] The curvature tensor is related to the affine connection on the manifold, which has to do with how nearby tangent spaces relate to each other. The Lie derivative on the other hand does not depend on any connection, only on the pullback using the flow of a local vector field. You therefore should generally not expect the two concepts to be related. While both the connection and the Lie derivative have several properties that you would typically associate with a derivative, only the connection is a natural directional derivative as ##\nabla_{fX} Y = f \nabla_X Y##, where ##f## is a scalar function. This does not hold for the Lie derivative. [/QUOTE]
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Forums
Physics
Special and General Relativity
Lie derivative and Riemann tensor
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