Gauss-Codazzi equations

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Gauss-Codazzi equations

[¦gau̇s kō′dat·sē i‚kwā·zhənz]
(mathematics)
Equations dealing with the components of the fundamental tensor and Riemann-Christoffel tensor of a surface.
References in periodicals archive ?
Interchanging X and Y here and using the Codazzi equation, we get
where A is a symmetric (1,1)-tensor, is equivalent to the Gauss and Codazzi equations and therefore to an isometric immersion of ([M.
cr]) [not equal to] 0, the second of Codazzi equations (3) and the Ricci equation (4) follow from (1) and the first of Codazzi (2).