The Gauss equations state that if 
is a regular patch on a regular
surface in 
with normal 
,
then
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
,
, and 
are coefficients of the second fundamental
form and 
are Christoffel symbols of the second
kind.
