Open problems and questions about geodesics

TL;DR

This paper surveys unresolved issues and questions concerning geodesics across various geometric structures such as Riemannian, Finsler, semi-Riemannian, and magnetic manifolds, highlighting key open problems in the field.

Contribution

It provides a comprehensive overview of open problems related to geodesics in different geometric contexts, serving as a resource for future research directions.

Findings

Identifies key open problems in geodesic theory.

Highlights differences between various geometric structures.

Suggests directions for future research in geodesic studies.

Abstract

The paper surveys open problems and questions related to geodesics defined by Riemannian, Finsler, semi Riemannian and magnetic structures on manifolds.