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单词 Monge Patch
释义

Monge Patch

A Monge patch is a Patch of the form

(1)

where 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.


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