what does following matrix says geometrically Let $M\subset \mathbb C^2$ be a hypersurface defined by $F(z,w)=0$. Then for some point $p\in M$, I've
$$\text{ rank of }\left(
    \begin{array}{ccc}
     0 &\frac{\partial F}{\partial z} &\frac{\partial F}{\partial w} \\
 \frac{\partial F}{\partial z} &\frac{\partial^2 F}{\partial ^ 2z} &\frac{\partial^2 F}{\partial z\partial w} \\
 \frac{\partial F}{\partial w} &\frac{\partial^2 F}{\partial w\partial z} &  \frac{\partial^2 F}{\partial w^2} \\
                    \end{array}
                  \right)_{\text{ at p}}=2.$$
What does it mean geometrically? Can anyone give a geometric picture near $p$? 
Any comment, suggestion, please.
Edit: Actually I was reading about Levi flat points and Pseudo-convex domains.  I want to understand the relation between these two concepts. A point p for which the rank of the above matrix is 2 is called Levi flat. If the surface is everywhere Levi flat then it is locally equivalent to $(0,1)\times \mathbb{C}^n$, so I have many examples....but what will happen for others for example take the three sphere in $\mathbb{C}^2$ given by $F(z,w)=|z|^2+|w|^2−1=0$.  This doesn't satisfy the rank 2 condition.  Can I have precisely these two situations?

Let $p=(z_0,w_0)$ and define
$G(z,w)=F(z,w)-(z_0,w_0)$.
Then the matrix is
$$
\left(
\begin{matrix}
  G   &  G_z    &  G_w      \cr
  G_z & (G_z)_z & (G_z)_w \cr
  G_w & (G_w)_z & (G_w)_w \cr
\end{matrix}
\right)_{\text{at }p}
$$
Since $G(p)=0$.
Is that any help?
