Question: PLEASE ANSWER ALL THESE QUESTIONS P2. (a) [7 points] For smooth functions f and g and for a smooth vector field X, show that L

PLEASE ANSWER ALL THESE QUESTIONS

P2. (a) [7 points] For smooth functions f and g and for a smooth vector field X, show that L x ( fg) = (2 xf )g + f(2 xg). (b) [7 points Show that, for smooth vector fields X and Y, the mapping Oxy : Co(M) - Co(M) f .> L x L y f - L y L xf is a derivation, i.e., it satisfies Oxy (f g) = (Oxy (f) )g + f(0x,y(g))

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