Monge Patch
A Monge patch is a Patch 
of the form
 | (1) |
is an Open Set in 
and 
is a differentiable function. The coefficients of thefirst 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) |
See also Monge's Form, Patch
References
Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 305-306, 1993.
- Functional
- Functional Analysis
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