Geodesic
Periods and principal parts of quadratic differentials on a rigged Riemann surface
Izvestiya. Mathematics, Tome 11 (1977) no. 6, pp. 1359-1375 
A. N. Tyurin. Periods and principal parts of quadratic differentials on a rigged Riemann surface. Izvestiya. Mathematics, Tome 11 (1977) no. 6, pp. 1359-1375. http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a8/
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     title = {Periods and principal parts of quadratic differentials on a~rigged {Riemann} surface},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we prove that the periods and principal parts uniquely determine a quadratic differential on a rigged Riemann surface. Bibliography: 7 titles.

[1] Appell P., Goursat E., Theorie des functions algebraiques et de leurs integrates, 2, Gauthiers-Villars, 1930.

[2] Atiyah M. F., “Complex analytic connections in fibre bundles”, Trans. Amer. Math. Soc., 85:1 (1957), 181–207 | DOI | MR | Zbl

[3] Hawley H., Schiffer M., “Half-order differentials on Riemann surfaces”, Acta Math., 115 (1966), 199–236 | DOI | MR | Zbl

[4] Gunning R. C., “Special coordinate covering of Riemann surfaces”, Math. Ann., 170 (1967), 67–86 | DOI | MR | Zbl

[5] Gunning R. C., “Analytic structures on the space of flat vector bundles over a compact Riemann surface”, Several Complex Variables (Maryland, 1970), Lecture Notes in Math., 185, Springer-Verlag, 1971 | MR

[6] Pohl W. F., “Differential geometry of higher order”, Topology, 1 (1962), 169–213 | DOI | MR

[7] Poincare H., “Sur les groups des equations lineaires”, Acta Math., IV (1901), 201–312 | MR

[8] Tyurin A. N., “Geometriya modulei vektornykh rassloenii”, Uspekhi matem. nauk, 29:6 (1974), 59–88 | MR | Zbl