Guardat en:
| Autors principals: | , |
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| Format: | Preprint |
| Publicat: |
2020
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2004.10185 |
| Etiquetes: |
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Taula de continguts:
- We present new explicit tight and overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible. Our proofs are based on the construction of nonvanishing curl eigenfields using suitable families of Jacobi or trigonometric polynomials. As a consequence, we show that the contact sphere theorem of Etnyre, Komendarczyk and Massot (2012) does not hold for weakly compatible metric as it was conjectured. We also establish a geometric rigidity for tight contact structures by showing that any contact form on the 3-sphere admitting a compatible metric that is the round one is isometric, up to a constant factor, to the standard (tight) contact form.