The Fundamental Theorem for locally projective geometries

TL;DR

This paper extends the Fundamental Theorem of Projective Geometry to locally projective and affino-projective geometries, including classical geometries like M"obius, Laguerre, and Minkowski, for dimensions three and higher, and non-bijective maps.

Contribution

It generalizes the Fundamental Theorem to a broader class of geometries and non-bijective transformations, expanding the theoretical framework.

Findings

Extended the theorem to locally projective geometries

Included non-bijective maps in the generalization

Covered classical geometries like M"obius, Laguerre, Minkowski

Abstract

We deal with generalizations of the Fundamental Theorem of Projective Geometry to other related geometries (of dimension $\geq 3$) and non bijective maps. We consider locally projective geometries and locally affino-projective geometries (which include the classical M\"obius, Laguerre and Minkowski geometries).