法向和切向的关系

$$\begin{array}{rl}dz=& \frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy\\ =& (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})\cdot (dx,dy)\\ =& dC=0\end{array}$$

前面是 法向量，后面是 切向量

升高一维就是空间了