# Changes

## Curvature is tensorial

, 17:36, 6 January 2012
Facts used
| 2 || The Leibniz-like axiom that is part of the definition of a connection || For a function [itex]f[/itex] and vector fields [itex]A,B[/itex], and a connection [itex]\nabla[/itex], we have [itex]\nabla_A(fB) = (Af)(B) + f\nabla_A(B)[/itex]
|-
| 3 || [[uses::Corollary of Leibniz rule for Lie bracket]] (in turn follows from [[uses::leibniz Leibniz rule for derivations]]|| For a function [itex]f[/itex] and vector fields [itex]X,Y[/itex]:
<br>[itex]\! f[X,Y] = [fX,Y] + (Yf)X[/itex]<br>[itex]\! f[X,Y] = [X,fY] - (Xf)Y[/itex]
|}