Contact structures and Beltrami fields on the torus and the sphere
نویسندگان
چکیده
We present new explicit tight and overtwisted contact structures on the (round) 3-sphere (flat) 3-torus for which ambient metric is weakly compatible. Our proofs are based construction of nonvanishing curl eigenfields using suitable families Jacobi or trigonometric polynomials. As a consequence, we show that sphere theorem Etnyre, Komendarczyk Massot (2012) does not hold compatible as it was conjectured. also establish geometric rigidity by showing any form admitting round one isometric, up to constant factor, standard (tight) form.
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2023
ISSN: ['1943-5258', '0022-2518', '1943-5266']
DOI: https://doi.org/10.1512/iumj.2023.72.9066