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quasar987
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Dec16-11, 07:41 AM
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There is one Levi-Civita connection for each metric. But even different metrics can have the same Levi-Civita connection: for any positive constant c, the two metrics g and cg have the same Levi-Civita connection because it is easy to see that the Levi-Civita connection of g also is compatible with cg.