A family of flat Minkowski planes over convex functions

TL;DR

This paper introduces a new family of flat Minkowski planes constructed via convex functions, expanding the understanding of their automorphism groups and classifying their isomorphism types.

Contribution

It presents a novel construction of flat Minkowski planes using convex functions and analyzes their automorphism groups and classification.

Findings

Automorphism groups are at least 3-dimensional.

Automorphism groups include a direct product of nd omponents.

Classifies isomorphism classes and automorphisms.

Abstract

Using suitable convex functions, we construct a new family of flat Minkowski planes whose automorphism groups are at least $3$-dimensional. These planes admit groups of automorphisms isomorphic to the direct product of $\mathbb{R}$ and the connected component of the affine group on $\mathbb{R}$. We also determine isomorphism classes, automorphisms and possible Klein-Kroll types for our examples.