Simple closed geodesics on regular tetrahedra in spaces of constant curvature

TL;DR

This survey explores the properties and behavior of simple closed geodesics on regular tetrahedra within three-dimensional spaces of constant curvature, summarizing recent research findings.

Contribution

It compiles and reviews existing results on geodesics on regular tetrahedra in curved spaces, highlighting key behaviors and open questions.

Findings

Characterization of simple closed geodesics

Behavior patterns in different curvature spaces

Summary of recent research advances

Abstract

In this survey results on the behavior of simple closed geodesics on regular tetrahedra in three-dimensional spaces of constant curvature are presented.