Isoperiodic foliation on the space of meromorphic real- normalized differentials

We study spaces of meromorphic differentials on complex curves, such that all their periods are real. Such differentials are referred to as real-normalized, they were introduced in the works of I.Krichever. The spaces of real-normalized differentials with the prescribed set of poles and residues at them may be stratified by the orders of the zeroes of the differentials. Differentials with the prescribed group of periods compose isoperiodic subspaces, respecting such stratification. In tis talk I plan to describe isoperiodic subspaces in the space of real-normalized differentials with a single pole of order two in the stratum where all the zeroes have order one.