Castling transformations of projective structures

TL;DR

This paper constructs an infinite sequence of projectively flat manifolds using castling transformations of prehomogeneous vector spaces and classifies those obtainable through finite transformations.

Contribution

It introduces a method to generate and classify flat projective structures via castling transformations, expanding understanding of such manifolds.

Findings

Infinite sequence of projectively flat manifolds constructed

Classification of manifolds with flat projective structures obtained by castling transformations

Description of these structures by atlases

Abstract

We construct an infinite sequence of projectively flat manifolds by using castling transformations of prehomogeneous vector spaces. We also give a classification of manifolds equipped with a flat projective structure obtained by a finite number of castling transformations, and describe these flat projective structures by atlases.