BIHARMONIC W-SURFACES IN 4-DIMENSIONAL PSEUDO-EUCLIDEAN SPACE

Abstract

In this article, W-surface in a 4-dimensional pseudo-Euclidean space E_t⁴ (t = l, 2) is defind and a classification problem of biharmonic W-surfaces in E_t⁴ 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_t⁴ is obtained. It is a generalization of main theorem in [7].