Mainardi-Codazzi Equations
 |  |  | (1) |
 | |  | (2) |
where
, 
, and 
are coefficients of the second Fundamental Form and 
areChristoffel Symbols of the Second Kind. Therefore, | |  | (3) |
 | |  | (4) |
 | |  | (5) |
 | |  | (6) |
 | |  | (7) |
 | |  | (8) |
where
, 
, and 
are coefficients of the first Fundamental Form.
References
Gray, A. ``The Mainardi-Codazzi Equations.'' §20.4 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 401-402, 1993.
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