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- dbpedia:GaussâCodazzi_equations
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In Riemannian geometry, the Gauss–Codazzi–Mainardi equations are fundamental equations in the theory of embedded hypersurfaces in a Euclidean space, and more generally submanifolds of Riemannian manifolds. They also have applications for embedded hypersurfaces of pseudo-Riemannian manifolds.In the classical differential geometry of surfaces, the Gauss–Codazzi–Mainardi equations consist of a pair of related equations.