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In this article, $ W $-surface in a 4-dimensional pseudo-Euclidean space $ E_t^4 $ ($ t = 1,2 $) is defined and a classification problem of biharmonic $ W $-surfaces in $ E_t^4 $ is investigated. The ...study of biharmonic submanifold in a pseudo-Euclidean space is an off-spring of the study of a problem "Classify all of finite type submanifolds in a Euclidean space $E^m " $ proposed by B. Y. Chen (see [5], [6] and [11]). As a result, one classification theorem for biharmonic $ W $-surfaces with flat normal connection in $ E_t^4 $ is obtained. It is a generalization of main theorem in [7].show more
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