Zoll manifolds with boundary

TL;DR

This paper investigates the geometric and topological properties of Zoll manifolds with boundary, focusing on those where all orthogonal geodesics to the boundary are closed and return orthogonally.

Contribution

It characterizes Zoll manifolds with boundary, extending classical results to include boundary conditions and orthogonal geodesic properties.

Findings

Identification of conditions for Zoll manifolds with boundary

Characterization of geodesic behavior at the boundary

Topological implications for manifolds with orthogonal geodesics

Abstract

In this paper we study the geometry and topology of compact Riemannian manifolds $(M,g)$ with boundary having the property that every geodesic that starts orthogonally to $\partial M$ also arrives orthogonally to the boundary.