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Unformatted text preview: X is equal to L X f = X ( f ) . • In local coordinates L X f = X i ∂ i f . • Deﬁnition 5.2.2 Let α be a 1form on M. The Lie derivative of α with respect to X is a 1form L X α deﬁned by ( L X α ) x = lim t → 1 t ² ϕ * t α ϕ t ( x )α x ³ = d dt ( ϕ * t α ) x ± ± ± ± t = • We can immediately generalize this to pforms. • Deﬁnition 5.2.3 Let α be a pform on M. The Lie derivative of α with respect to X is a pform L X α deﬁned by ( L X α ) x = lim t → 1 t ² ϕ * t α ϕ t ( x )α x ³ = d dt ( ϕ * t α ) x ± ± ± ± t = di ﬀ geom.tex; April 12, 2006; 17:59; p. 112...
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 Spring '10
 Wong
 Geometry, Derivative

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