An analogue of the Rauch variational formula for Prym differentials (Q910891)

Using some of \textit{R. S. Hamilton}'s techniques [see his Thesis ``Variation of structure on Riemann surfaces'', Princeton Univ. Press, 1966 and \textit{C. J. Earle}'s paper in ``Differential geometry and complex analysis, Vol. Dedic. E. H. Rauch, 15-31 (1985; Zbl 0568.01021)], the author find an analogue of Rauch's formula for the first variation of the Prym differentials. He also explains the difference between the Prym case and the classical case of abelian differentials where the character is its inverse (for the Prym character, it is not true).