DOI: 10.1007/s13324-016-0126-8">
 

Integrability conditions on a sub-Riemannian structure on S3

Document Type

Article

Publication Date

2017

Department/School

Mathematics

Publication Title

Analysis and Mathematical Physics

Abstract

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.

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DOI: 10.1007/s13324-016-0126-8

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