Abstract
Spatial surfaces with parallel mean curvature vector in pseudo-Euclidean spaces of arbitrary dimension and index were classified by B.Y. Chen. In this work, we give a complete classification of Lorentzian surfaces with parallel mean curvature vector in pseudo-Euclidean spaces of arbitrary dimension and index. Consequently, the problem to classify all the surfaces with parallel mean curvature vector in pseudo-Euclidean spaces has been solved.
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