A Monge patch is a patch 
of the form
 |
(1)
|
where 
is an open set
in 
and 
is a differentiable function. The coefficients of
the first fundamental form are given by
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
and the second fundamental form by
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
For a Monge patch, the Gaussian curvature and mean curvature are
 |  |  |
(8)
|
 |  |  |
(9)
|
