Corpus ID: 216036323

Contact structures and Beltrami fields on the torus and the sphere.

@article{PeraltaSalas2020ContactSA,
  title={Contact structures and Beltrami fields on the torus and the sphere.},
  author={Daniel Peralta-Salas and Radu Slobodeanu},
  journal={arXiv: Differential Geometry},
  year={2020}
}
  • Daniel Peralta-Salas, Radu Slobodeanu
  • Published 2020
  • Mathematics, Physics
  • arXiv: Differential Geometry
  • 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… CONTINUE READING