• Corpus ID: 245218459

Pseudo-K\"ahler geometry of properly convex projective structures on the torus

@inproceedings{Rungi2021PseudoKahlerGO,
  title={Pseudo-K\"ahler geometry of properly convex projective structures on the torus},
  author={Nicholas Rungi and Andrea Tamburelli},
  year={2021}
}

• Nicholas Rungi, Andrea Tamburelli
• Published 16 December 2021
• Mathematics

In this paper we prove the existence of a pseudo-Kähler structure on the deformation space B0pT q of properly convex RP-structures over the torus. In particular, the pseudo-Riemannian metric and the symplectic form are compatible with the complex structure inherited from the identification of B0pT q with the complement of the zero section of the total space of the bundle of cubic holomorphic differentials over the Teichmüller space. We show that the S-action on B0pT q, given by rotation of the fibers, is Hamiltonian and it preserves both the metric and the symplectic form. Finally, we prove the existence of a moment map for the SLp2,Rq-action over B0pT q.