An extension of Wolpert's derivative formula

Abstract

A well known formula of Wolpert expresses the derivative of length of a geodesic γ on a hyperbolic surface with respect to the Fenchel Nielsen twist about a fixed simple geodesic C as a sum of the cosines of the intersection angles between the two curves. We derive an analogous formula for the derivative of the length of γ with respect to variation of the length of the fixed curve C.