Integrability conditions on a sub-Riemannian structure on $$\mathbb {S}^3$$

Calin, O., Chang, D.C.: Sub-Riemannian geometry. General theory and examples, encyclopedia of mathematics and its applications. Cambridge University Press, Cambridge (2009)

Calin, O., Chang, D.C.: Geometric mechanics on Riemannian manifolds: applications to partial differential equations. Applied and numerical analysis. Birhäuser, Boston (2004)

Calin, O., Chang, D.C., Eastwood, M.: Integrability conditions for the Grushin and Martinet distributions. Bull. IMAS New Ser. 2, 159–168 (2013)

Calin, O., Chang, D.C., Eastwood, M.: Integrability conditions for Heisenberg and Grushin-type distributions. Anal. Math. Phys. 4, 99–114 (2014)

Calin, O., Chang, D.C., Hu, J.: A Poincaré lemma for the Heisenberg group. Adv. Appl. Anal. 60, 90–102 (2014)

Calin, O., Chang, D.C., Hu, J.: Integrability conditions on Engel-type manifolds. Anal. Math. Phys. 5(3), 217–231 (2015)

Calin, O., Chang, D.C., Markina, I.: SubRiemannian geometry on the sphere $$\mathbb{S}^3$$. Can. J. Math. 61(4), 721–739 (2009)

Hörmander, L.: Hypo-elliptic second order differential equations. Acta Math. 119, 147–171 (1967)

Wolfram Research Inc, Mathematica, Version 10.3, Champaign, IL (2015)