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Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces. (arXiv:1711.03429v1 [math.GT])
来源于:arXiv
A well-known theorem of Wolpert shows that the Weil-Petersson symplectic form
on Teichm\"uller space, computed on two infinitesimal twists along simple
closed geodesics on a fixed hyperbolic surface, equals the sum of the cosines
of the intersection angles. We define an infinitesimal deformation starting
from a more general object, namely a balanced geodesic graph, by which any
tangent vector to Teichm\"uller space can be represented. We then prove a
generalization of Wolpert's formula for these deformations. In the case of
simple closed curves, we recover the theorem of Wolpert. 查看全文>>