Let 
be a unit tangent vector of a regular
surface 
.
Then the normal curvature of 
in the direction 
is
 |
(1)
|
where 
is the shape operator. Let 
be a regular surface,
, 
be an injective regular patch
of 
with 
,
and
 |
(2)
|
where 
.
Then the normal curvature in the direction 
is
 |
(3)
|
where 
,
, and 
are the coefficients of the first fundamental
form and 
,
, and 
are the coefficients of the second fundamental
form.
The maximum and minimum values of the normal curvature at a point on a regular surface
are called the principal curvatures 
and 
.
