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Highlights Surfaces constructed using a given timelike curve Constraints for surfaces to have constant mean curvature along the given curve are obtained The method is illustrated with examples Graphical Abstract We construct surfaces with constant mean curvature through a given timelike curve. Figure. A surface with constant mean curvature along a given timelike curve (red in colour). Aim The aim of this paper is to construct surfaces with constant mean curvature through a givendoi:10.2339/politeknik.870539 fatcat:odrpch73vbceznffva53e3twmq