The geometry of a positively curved Zoll surface of revolution

TL;DR

This paper explores the geometric properties of Zoll surfaces with positive curvature, focusing on the structure of their geodesic manifolds, and demonstrates how these induce Finsler metrics with constant flag curvature, including explicit examples.

Contribution

It provides new insights into the geometry of Zoll surfaces of positive curvature and constructs explicit Finsler metrics of constant flag curvature derived from them.

Findings

Manifolds of geodesics of Zoll surfaces are characterized.

Induction of Finsler metrics with constant flag curvature from Zoll surfaces.

Explicit constructions of such Finsler metrics.

Abstract

In this paper, we study the geometry of the manifolds of geodesics of a Zoll surface of positive Gauss curvature, show how these metrics induce Finsler metrics of constant flag curvature and give some explicit constructions.