6 papers · 1 filter
Equiaffine immersions and pseudo-Riemannian space forms
Nicholas Rungi
We introduce an explicit construction that produces immersions into the pseudosphere and the pseudohyperbolic space starting from equiaffi…
Para-complex geometry and cyclic Higgs bundles
Nicholas Rungi, Andrea Tamburelli
We introduce para-complex and pseudo-Riemannian geometric methods for the study of representations of surface groups in . For our techniques all…
Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and -quasi-Fuchsian representations
Nicholas Rungi, Andrea Tamburelli
In this paper we introduce complex minimal Lagrangian surfaces in the bi-complex hyperbolic space and study their relation with representations in . Our…
The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space
Nicholas Rungi, Andrea Tamburelli
We study the moduli space of flat maximal space-like embeddings in from various aspects. We first describe the associated Codazzi tensors to the embedding in the…
Riemannian geometry of maximal surface group representations acting on pseudo-hyperbolic space
Nicholas Rungi
For any maximal surface group representation into , we introduce a non-degenerate scalar product on the the first cohomology group of the surface with values…
Pseudo-Kähler structure on the -Hitchin component and Goldman symplectic form
Nicholas Rungi, Andrea Tamburelli
The aim of this paper is to show the existence and give an explicit description of a pseudo-Riemannian metric and a symplectic form on the -Hitc…