McMullen, Curtis2014-03-112014-03-11McMullen, Curtis T. 2012. “Moduli Spaces of Isoperiodic Forms on Riemann Surfaces.” Working paper, Department of Mathematics, Harvard University.http://nrs.harvard.edu/urn-3:HUL.InstRepos:11880197This paper describes the intrinsic geometry of a leaf \(\mathcal{A}(L)\) of the absolute period foliation of the Hodge bundle \(\Omega \bar{M}_g\): its singular Euclidean structure, its natural foliations and its discretized Teichmuller dynamics. We establish metric completeness of \(\mathcal{A}(L)\) for general g, and then turn to a study of the case g = 2. In this case the Euclidean structure comes from a canonical meromorphic quadratic differential on \(\mathcal{A}(L) \cong \mathbb{H}\), whose zeros, poles and exotic trajectories are analyzed in detail.en-USJournal Article2014-03-1110.1215/00127094-2785588