On complex structures on two-dimensional tori admitting metrics with nontrivial quadratic integral

In this paper the set of complex structures on a torus admitting Riemannian metrics (consistent with these complex structures) with nontrivial quadratic integrals is described. Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 643–652, November, 1995. This work was partially supported by the Volkswagen Fund and was mainly carried out at Bochum University (Germany). The authors are grateful to Bochum University for its hospitality.