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Levi-Civita connection

259 bytes added, 21:02, 24 July 2009
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<math>g(\nabla_XY,Z) = \frac{Xg(Y,Z) + Yg(Z,X) - Zg(X,Y) + g(Y,[Z,X]) + g(Z,[X,Y]) - g(X,[Y,Z])}{2}</math>.
===Additional use===
The term '''Levi-Civita connection''' is sometimes also used for the connection induced on any tensor product involving the tangent and cotangent bundle, using the rule for [[tensor product of connections]] and the [[dual connection]].
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