Nicholas Rungi

activity

20212026

collaborators

9 papers

math.DG2026

Extending Donaldson's HyperKähler Structure via Minimal Surfaces into $PSL (2, C)$

Christian El Emam, Filippo Mazzoli, Nicholas Rungi +2

We construct a deformation space for minimal immersions into $PSL (2, C)$ with its holomorphic Killing form, and define an explicit, mapping class group invariant,…

math.DG2025

Equiaffine immersions and pseudo-Riemannian space forms

Nicholas Rungi

We introduce an explicit construction that produces immersions into the pseudosphere $S^{n, n + 1}$ and the pseudohyperbolic space $H^{n + 1, n}$ starting from equiaffi…

math.DG2025

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 $SL (2 m + 1, R)$ . For $m = 1$ our techniques all…

math.DG2024

Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and $SL (3, C)$ -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 $SL (3, C)$ . Our…

math.DG2023

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 $H^{2, 2}$ from various aspects. We first describe the associated Codazzi tensors to the embedding in the…

math.DG2023

Riemannian geometry of maximal surface group representations acting on pseudo-hyperbolic space

Nicholas Rungi

For any maximal surface group representation into $SO_{0} (2, n + 1)$ , we introduce a non-degenerate scalar product on the the first cohomology group of the surface with values…

math.DG2023

Pseudo-Kähler structure on the $SL (3, R)$ -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 $SL (3, R)$ -Hitc…

math.SG2022

Global Darboux coordinates for complete Lagrangian fibrations and an application to the deformation space of $R P^{2}$ -structures in genus one

Nicholas Rungi, Andrea Tamburelli

In this paper we study a broad class of complete Hamiltonian integrable systems, namely the ones whose associated Lagrangian fibration is complete and has non compact fibres. By st…

math.DG2021

Pseudo-Kähler geometry of properly convex projective structures on the torus

Nicholas Rungi, Andrea Tamburelli

In this paper we prove the existence of a pseudo-Kähler structure on the deformation space $B_{0} (T^{2})$ of properly convex $R P^{2}$ -structures over the torus.…

Extending Donaldson's HyperKähler Structure via Minimal Surfaces into PSL(2,C)

Equiaffine immersions and pseudo-Riemannian space forms

Para-complex geometry and cyclic Higgs bundles

Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and SL(3,C)-quasi-Fuchsian representations

The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space

Riemannian geometry of maximal surface group representations acting on pseudo-hyperbolic space

Pseudo-Kähler structure on the SL(3,R)-Hitchin component and Goldman symplectic form

Global Darboux coordinates for complete Lagrangian fibrations and an application to the deformation space of RP2-structures in genus one

Pseudo-Kähler geometry of properly convex projective structures on the torus

Extending Donaldson's HyperKähler Structure via Minimal Surfaces into $PSL (2, C)$

Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and $SL (3, C)$ -quasi-Fuchsian representations

Pseudo-Kähler structure on the $SL (3, R)$ -Hitchin component and Goldman symplectic form

Global Darboux coordinates for complete Lagrangian fibrations and an application to the deformation space of $R P^{2}$ -structures in genus one