Hello,


$CR$ manifold for example $S^1\times C^{n-1}$ is every where levi flat. Can I have example of $CR$ manifold which has at least one non levi flat point.


I can't see what the happening in Non-Levi flat points. Sorry for vague question and if it is trivial.. .... but basically i want to understand the non levi flat point such that i can easily determine all non levi flat point of given CR manifold...


Any comment and suggestion are welcome.. Thanks in advance.



What does non-levi flat point mean geometrically
Probably the most easy example to understand is the round sphere in $\mathbb{C}^2$. It is strictly convex, so that in particular it is strictly pseudo-convex, and very not Levy-flat.


For a submanifold $M$, Levy flatness is equivalent to the integrability of $TM\cap i TM$. If you compute this plane distribution in the case of the unit sphere, you will see that it is the orthogonal to the Hopf fibration, and in particular as far from being integrable as possible.


This is short, but I hope there are sufficient key words so that you can study the subject more deeply in books.


