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.
Gauss Equations
See also
Christoffel Symbol of the Second Kind, Fundamental Forms, Peterson-Mainardi-Codazzi EquationsExplore with Wolfram|Alpha
References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 511-512, 1997.Referenced on Wolfram|Alpha
Gauss EquationsCite this as:
Weisstein, Eric W. "Gauss Equations." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GaussEquations.html