304 research outputs found
Dependence of the Gauss-Codazzi equations and the Ricci equation of Lorentz surfaces
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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