Webs and projective structures on a plane

TL;DR

This paper establishes a correspondence between certain projective structures on a plane and Veronese webs, using this link to characterize these structures via second order ordinary differential equations.

Contribution

It introduces a novel correspondence between projective structures with skew-symmetric Ricci tensor and Veronese webs, providing a new characterization through second order ODEs.

Findings

Correspondence between projective structures and Veronese webs

Characterization of structures via second order ODEs

Insight into geometric structures on a plane

Abstract

We prove that there is a correspondence between projective structures defined by torsion-free connections with skew-symmetric Ricci tensor and Veronese webs on a plane. The correspondence is used to characterise the projective structures in terms of second order ODEs.