This paper deals with integrability conditions for a sub-Riemannian system of equations for a step 2 distribution on the sphere $$\mathbb {S}^3$$ S 3 . We prove that a certain sub-Riemannian system $$Xf =a$$ X f = a , $$Yf =b$$ Y f = b on $$\mathbb {S}^3$$ S 3 has a solution if and only if the following integrability conditions hold: $$X^2 b + 4b = (XY + [X, Y]) a $$ X 2 b + 4 b = ( X Y + [ X , Y ] ) a , $$Y^2 a + 4a = (YX-[X, Y]) b$$ Y 2 a + 4 a = ( Y X - [ 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.
Analysis and Mathematical Physics – Springer Journals
Published: Feb 13, 2016
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.