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.
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.
Weisstein, Eric W. "Gauss Equations." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/GaussEquations.html