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The fundamental equations of Gauss, Codazzi and Ricci provide the conditionsfor local isometric embeddability. In general, the three fundamental equationsare independent for surfaces in Riemannian 4-manifolds. In contrast, we provein this article that for arbitrary Lorentz surfaces in Lorentzian Kaehlersurfaces the equation of Ricci is a consequence of the equations of Gauss andCodazzi.

Dependence of the Gauss-Codazzi equations and the Ricci equation of Lorentz surfaces