Isoperiodic foliation on the moduli spaces of real-normalized differentials with a single pole

Meromorphic differentials on Riemann surfaces are said to be real-normalized if all their periods are real. Moduli spaces of real-normalized differentials on Riemann surfaces of given genus with prescribed orders of their poles and residues admit a stratification by the orders of zeroes of the differentials. Subsets of real-normalized differentials with a fixed polarized module of periods compose isoperiodic subspaces, which also admit this stratification. In this work, we prove connectedness of the principal stratum for the isoperiodic subspaces in the space of real-normalized differentials with a single pole of order two when all the periods are incommesurable.