Integrability conditions on a sub-Riemannian structure on S3
Analysis and Mathematical Physics
This paper deals with integrability conditions for a sub-Riemannian system of equations for a step 2 distribution on the sphere S3. We prove that a certain sub-Riemannian system Xf= a, Yf= b on S3 has a solution if and only if the following integrability conditions hold: X2b+ 4 b= (XY+ [ X, Y]) a, Y2a+ 4 a= (YX- [ X, Y]) b. We also provide an explicit construction of the solution f in terms of the vector fields X, Y and functions a and b.
Link to Published Version
Calin, O., Chang, D.-C., & Hu, J. (2017). Integrability conditions on a sub-Riemannian structure on S3. Analysis and Mathematical Physics, 7(1), 9–18. https://doi.org/10.1007/s13324-016-0126-8