Grafting of real projective surfaces with Hitchin holonomy

TL;DR

This paper introduces graftable curves on real projective surfaces, constructs examples in the Hitchin case, and demonstrates that structures with identical Hitchin holonomy and weight type are interconnected through multi-graftings.

Contribution

It defines graftable curves on real projective surfaces and shows their role in relating structures with the same Hitchin holonomy via multi-graftings.

Findings

Constructed graftable curves in the Hitchin case

Established relation between structures with same Hitchin holonomy

Demonstrated multi-grafting connects such structures

Abstract

We define graftable curves on real projective surfaces. In particular, we construct graftable ones in Hitchin case and show that real projective structures with the same Hitchin holonomy, carrying the same weight type, are related to each other via multi-graftings.