#### Differential equation of principal section/direction

Let be a surface and be the principal curvature, then

or

Then, differentiating w r. to. duanddv separately, we get

and

Eliminating from (i) and (ii) we get

or
(i)

which is the required equation of principal directions.

Note

The equation of principal directions is

#### Example

Find principal sections on hyperboloid at origin

Solution