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 given

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... curve Design &Methodology We construct surfaces using the Frenet frame of the given timelike curve and obtain conditions. Originality The study is original. Findings We find constraints on surfaces to have a constant mean curvature along a given timelike curve. Conclusion It is possible to obtain surfaces with constant mean curvature along a given timelike curve. ABSTRACT We construct surfaces with constant mean curvature through a given timelike curve. We show that, it is possible to obtain such surfaces for any given timelike curve. The validity of the method supported with illustrative examples.