Singular Euclidean Structure
A holomorphic quadratic differential determines a Riemannian metric on the complement of its zeroes. If is defined on a domain in the complex plane and, then the associated Riemannian metric is where . Since is holomorphic, the curvature of this metric is zero. Thus, a holomorphic quadratic differential defines a flat metric on the complement of the set of such that .
Read more about this topic: Quadratic Differential
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