Talk:Gauss–Codazzi equations

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Fundamental to submanifold geometry, this needs serious expansion. Geometry guy 20:52, 21 May 2007 (UTC)

[edit] Dump from Mainardi-Codazzi

Don't want to step on any tows. Luckily the article was new, and not much developed:

In differential geometry, the Mainardi-Codazzi equations relate the first fundamental form and the second fundamental form of a surface. Given a set of coefficents of the first and second fundamental forms, the Mainardi-Codazzi equations provide a simple method for determining whether a surface exists with that particular set of coefficients. The first fundamental form makes its appearance in terms of the Christoffel symbols:

$e_v-f_u=e\Gamma_{12}^1 + f(\Gamma_{12}^2-\Gamma_{11}^1) - g\Gamma_{11}^2$

$f_v-g_u=e\Gamma_{22}^1 + f(\Gamma_{22}^2-\Gamma_{12}^1) - g\Gamma_{12}^2$

Regards, Silly rabbit 00:43, 28 May 2007 (UTC)

Dear Rabbit, No problem. I didn't know an article already existed. I added the classical equations to this article. Jhausauer 01:51, 28 May 2007 (UTC)

Talk:Gauss–Codazzi equations

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[edit] Dump from Mainardi-Codazzi

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