Quadratic Differentials

A quadratic differential on aRiemann surface is locally represented by a ho­ lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con­ venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the