Some Remarks on the Lie Derivative and the Pullback Equation for Contact Forms

Given the contact forms f and g, and the 1-form h, we discuss the existence of a vector field u verifyingℒu⁢(f)=d⁢(u⁢⌟⁢f)+u⁢⌟⁢d⁢f=h.${\mathcal{L}_{u}(f\/)=d(u\,\lrcorner\,f\/)+u\,\lrcorner\,df=h.}$This is closely related to the pullback equation,where we seek for a diffeomorphism φ satisfyingφ∗⁢(f)=g.${\varphi^{\ast}(f\/)=g.}$

Abstract licence: CC BY

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