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 
.
