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Curvature is tensorial

No change in size, 17:36, 6 January 2012
Facts used
| 2 || The Leibniz-like axiom that is part of the definition of a connection || For a function <math>f</math> and vector fields <math>A,B</math>, and a connection <math>\nabla</math>, we have <math>\nabla_A(fB) = (Af)(B) + f\nabla_A(B)</math>
| 3 || [[uses::Corollary of Leibniz rule for Lie bracket]] (in turn follows from [[uses::leibniz Leibniz rule for derivations]]|| For a function <math>f</math> and vector fields <math>X,Y</math>:
<br><math>\! f[X,Y] = [fX,Y] + (Yf)X</math><br><math>\! f[X,Y] = [X,fY] - (Xf)Y</math>
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