A Counterexample to Guillemin's Zollfrei Conjecture

Abstract

We construct Zollfrei Lorentzian metrics on every nontrivial orientable circle bundle over a orientable closed surface. Further we prove a weaker version of Guillemin's conjecture assuming global hyperbolicity of the universal cover.

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References in corpus (2)

• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• Linking and causality in globally hyperbolic spacetimes

Cited by in corpus (4)

• Open problems and questions about geodesics
• Conformally embedded spacetimes and the space of null geodesics
• The space of light rays: Causality and $L$-boundary
• On the space of null geodesics of a spacetime: the compact case, Engel geometry and retrievability