## Monge Patch

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)