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Zoll manifolds with boundary

Eduardo Longa, Paolo Piccione, Roney Santos

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.

Zoll manifolds with boundary

Abstract

In this paper we study the geometry and topology of compact Riemannian manifolds with boundary having the property that every geodesic that starts orthogonally to also arrives orthogonally to the boundary.

Paper Structure

This paper contains 9 sections, 27 theorems, 17 equations.

Table of Contents

  1. Introduction
  2. Zoll manifolds with boundary and length of free boundary geodesics
  3. Degeneracy and Morse index
  4. Geometry of Zoll manifolds with boundary
  5. Zoll manifolds with disconnected boundary
  6. Zoll manifolds with connected boundary
  7. The projection map
  8. Topology of Zoll manifolds with connected boundary
  9. Constructions of Zoll manifolds with connected boundary

Key Result

Theorem 1.1

Let $(M,g)$ be a Zoll manifold with boundary. Then: Moreover:

Theorems & Definitions (52)

  • Theorem 1.1
  • Theorem 1.2
  • Proposition 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Definition 2.1
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • ...and 42 more