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Solving the same question two ways: Parallel transport vs. the Lie derivative
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[QUOTE="troglodyte, post: 6342495, member: 677299"] Hopefully it helps.If you put some specific objects in the Lie bracket you check whether this objects are commute or not.If [X,Y]=XY-YX =0 the Objects(here vectorfields) commute.This leads to XY=YX otherwise they don't commute.Maybe you can try to interpret the geometry with this new knowledge .You can also check Misner and Wheeler(Gravitation) for a good reference on this field or some nice older post on this board. [/QUOTE]
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Solving the same question two ways: Parallel transport vs. the Lie derivative
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