This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: X be a chart containing x ∈ X , since this is a diffeomorphism: ( f ◦ γ ) (0) = ( f ◦ φ ◦ φ1 ◦ γ ) (0) = ( ( f ◦ φ ) ◦ ( φ1 ◦ γ )) (0) , hence by the chain rule ( ( f ◦ φ ) ◦ ( φ1 ◦ γ )) (0) = ( f ◦ φ ) ( φ1 ( γ (0))) D ( φ1 ◦ γ ) (0) . 3. Using the terms of the last question, choosing the deﬁnition: h f,v i = ( f ◦ γ ) (0) = d dt ( f ◦ γ ) ( t ) ´ ´ ´ ´ t =0 , we can apply Leibnitz rule on the designated expression: h fg,v i = ( fg ◦ γ ) (0) = (( f ◦ γ ) ( g ◦ γ )) (0) = = g ( γ (0)) ( f ◦ γ ) (0) + f ( γ (0)) ( g ◦ γ ) (0) = = g ( x ) h f,v i + f ( x ) h g,v i 2...
View
Full Document
 Spring '09
 MICHAELPOLYAK
 Calculus, Geometry, Derivative, Gottfried Leibniz, Hava Shabtai

Click to edit the document details