The geodesics for Poincar\'e's half-plane: a nonstandard derivation

TL;DR

This paper presents a novel approach to deriving geodesics in Poincaré's half-plane using Noether-like transformations that are not based on symmetries, offering new insights into geometric properties.

Contribution

It introduces a nonstandard method for deriving geodesics through transformations unrelated to traditional symmetry groups, expanding the tools for geometric analysis.

Findings

Geodesics in Poincaré's half-plane can be derived without symmetry-based methods.

Noether-like transformations provide alternative insights into geometric properties.

The approach offers a new perspective on the relationship between transformations and geometric structures.

Abstract

Constants of motion are usually derived from groups of symmetry transformation of the system. Here we show that useful properties of the system can be deduced from a family of Noether-like transformations that are not inspired by any symmetry whatsoever. The system here is the Lagrangian interpretation of Poincar\'e's half plane, and the property is the shape of the geodesics.