A counterexample to Guillemin's Zollfrei conjecture (Q2852533)
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scientific article; zbMATH DE number 6214304
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counterexample to Guillemin's Zollfrei conjecture |
scientific article; zbMATH DE number 6214304 |
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9 October 2013
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Zollfrei metric
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Lorentzian manifold
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closed geodesic
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light-like curve
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circle bundle
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A counterexample to Guillemin's Zollfrei conjecture (English)
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This paper concerns Zollfrei metrics on compact 3-manifolds. As the main result, the author constructs Zollfrei Lorentzian metrics on every non-trivial orientable circle bundle over an orientable closed surface, and this provides a counterexample to \textit{V. Guillemin}'s conjecture [Ann. Math. Stud. 121 (1989; Zbl 0697.53003)]. On the other hand, it is shown that Guillemin's conjecture holds true under additional assumption on the global hyperbolicity of the universal covering of 3-manifolds in question.
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