Ir al contenido

Documat


Steady Euler Flows on the 3-Sphere and Other Sasakian 3-Manifolds

  • Slobodeanu, Radu [1]
    1. [1] University of Bucharest

      University of Bucharest

      Sector 3, Rumanía

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 1, 2021
  • Idioma: inglés
  • DOI: 10.1007/s12346-020-00440-y
  • Enlaces
  • Resumen
    • We present new steady Euler solutions on the (round) 3-sphere, that bifurcate from an ansatz proposed in, showing that these previously known solutions are not isolated. We also extend this ansatz to any Sasakian 3-manifold, such as the Heisenberg group and SL(2, R).

  • Referencias bibliográficas
    • 1. Arnold, V.I., Khesin, B.: Topological Methods in Hydrodynamics. Springer, New York (1998)
    • 2. Baird P.: Harmonic maps with symmetry, harmonic morphisms and deformations of metrics. Research Notes in Mathematics, vol. 87, Pitman,...
    • 3. Belgun, F.: Normal CR structures on compact 3-manifolds. Math. Z. 238, 441–460 (2001)
    • 4. Belgun, F.: Normal CR structures on S3. Math. Z. 244, 125–151 (2003)
    • 5. Boyer, C.P., Galicki, K.: Sasakian Geometry. Oxford University Press, Oxford (2008)
    • 6. Cartan, E.: Familles de surfaces isoparamétriques dans les espaces a courbure constante. Ann. Mat. Pura Appl. 17, 177–191 (1938)
    • 7. Constantin P., Joonhyun La, and Vicol, V.: Remarks on a paper by Gavrilov: Grad-Shafranov equations, steady solutions of the three dimensional...
    • 8. Enciso A., Peralta-Salas, D., and Torres de Lizaur, F.: Knotted structures in high-energy Beltrami fields on the torus and the sphere....
    • 9. Gavrilov A. V.: A steady smooth Euler flow with support in the vicinity of a helix, preprint arXiv:1906.07465 (2019)
    • 10. Geiges, H.: Normal contact structures on 3-manifolds. Tohoku Math. J. 49, 415–422 (1997)
    • 11. Khesin, B., Kuksin, S., Peralta-Salas, D.: KAM theory and the 3D Euler equation. Adv. Math. 267, 498–522 (2014)
    • 12. Khesin, B., Kuksin, S., Peralta-Salas, D.: Global, Local and Dense Non-mixing of the 3D Euler Equation. Arch. Rational Mech. Anal. 238,...
    • 13. Komendarczyk, R.: Tight Beltrami fields with symmetry. Geom. Dedicata. 134, 217–238 (2008)
    • 14. Münzner, H.F.: Isoparametrische Hyperflächen in Sphären. Math. Ann. 251, 57–71 (1980)
    • 15. Münzner H. F.: Isoparametrische Hyperflächen in Sphären II. Über die Zerlegung der Sphäre in Ballbündel, Math. Ann. 256, 215–232 (1981)
    • 16. Nomizu, K.: Elie Cartan’s work on isoparametric families of hypersurfaces. Proc. Symp. Pure Math. 27, 191–200 (1975)
    • 17. Peralta-Salas, D.: Selected topics on the topology of ideal fluid flows. Int. J. Geom. Methods Mod. Phys. 13, 1630012 (2016)
    • 18. Peralta-Salas, D., Slobodeanu, R.: Energy minimizing Beltrami fields on Sasakian 3-manifolds. Int. Math. Res. Not. (2019). https://doi.org/10.1093/imrn/rnz044
    • 19. Peralta-Salas, D., and Slobodeanu, R.: Contact structures and Beltrami fields on the torus and the sphere, preprint (2020), arXiv:2004.10185...
    • 20. Slobodeanu R.: Steady Euler flows and the Faddeev-Skyrme model with mass term, J. Math. Phys. 56 (2015): 023102; arXiv:1405.3469v3 [math.DG]
    • 21. Slobodeanu R.: A steady Euler flow on the 3-sphere and its associated Faddeev-Skyrme solution, Rev. Roumaine Math. Pures Appl. 65 (2020),...
    • 22. Thorbergsson, G.: A Survey on Isoparametric Hypersurfaces and their Generalizations, in Handbook of Differential Geometry, vol. I, pp....
    • 23. Wang, Qi-Ming, Isoparametric functions on Riemannian manifolds. I, Math. Ann. 277 (1987), 639 – 646
    • 24. Wolfram Research, Inc., Mathematica, Version 11.2, Champaign, IL (2017)

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno