304 research outputs found

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

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    The fundamental equations of Gauss, Codazzi and Ricci provide the conditions for local isometric embeddability. In general, the three fundamental equations are independent for surfaces in Riemannian 4-manifolds. In contrast, we prove in this article that for arbitrary Lorentz surfaces in Lorentzian Kaehler surfaces the equation of Ricci is a consequence of the equations of Gauss and Codazzi.Comment: 9 pages. Appeared in Publ. Math. Debrecen, 74 (2009), nos. 3-4, 341-34
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