A weaker geodesic completeness and Clifton-Pohl torus

TL;DR

This paper introduces a new complex-analytic definition of geodesic completeness and applies it to the Clifton-Pohl torus, linking geodesic completeness to an initial condition function called 'impulse'.

Contribution

It proposes a novel complex-analytic approach to geodesic completeness and analyzes the Clifton-Pohl torus within this framework.

Findings

Geodesic completeness is related to the impulse function.

The new definition provides insights into the Clifton-Pohl torus.

Analytic continuation in the complex domain is effective for studying geodesics.

Abstract

We propose a new definition of geodesic completeness, based on analytical continuation in the complex domain: we apply this idea to Clifton-Pohl torus, relating, for each geodesic, completeness to the value of a function of initial conditions, called 'impulse'.