Codazzi equation | Article about Codazzi equation by The Free Dictionary
Gauss-Codazzi equations (redirected from Codazzi equation)
Gauss-Codazzi equations[¦gau̇s kō′dat·sē i‚kwā·zhənz]
Equations dealing with the components of the fundamental tensor and Riemann-Christoffel tensor of a surface.
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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).