On closed geodesics in Lorentz manifolds
Souheib Allout, Abderrahmane Belkacem, Abdelghani Zeghib
TL;DR
This paper constructs examples of compact Lorentz manifolds that do not contain any closed geodesics, challenging assumptions about geodesic existence in such spaces.
Contribution
It provides the first known examples of compact Lorentz manifolds lacking closed geodesics, offering new insights into Lorentzian geometry.
Findings
Existence of compact Lorentz manifolds without closed geodesics
Counterexamples to common assumptions in Lorentzian geometry
Advancement in understanding geodesic properties in Lorentz manifolds
Abstract
We construct compact Lorentz manifolds without closed geodesics.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology · Ophthalmology and Eye Disorders