This preview shows pages 1–2. Sign up to view the full content.
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
This note was uploaded on 09/16/2009 for the course MATH 106723 taught by Professor Michaelpolyak during the Spring '09 term at Technion.
 Spring '09
 MICHAELPOLYAK
 Geometry

Click to edit the document details