We discuss the necessary and su‰cient conditions for the existence of Lorentzian stationary surfaces in 4-dimensional space forms of index 2, and isometric stationary deformations preserving normal curvature.

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Abstract. Let XN{c) denote the TV-dimensional simply connected space form of constant curvature c. We consider a problem to classify those minimal surfaces in XN(c) which are locally isometric to minimal surfaces in X*{c). In this paper we solve this problem in the case where N = 4 , and give a result also in higher codimensional cases.

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