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We calculated some Wilson loop functionals in a static sphere-symmetrical diagonal metric field, the Robertson–Walker (RW) metric field and a gravitational metric field established by cosmic string, respectively, and calculated the leading term W(2) and the term W(4) of a Wilson loop in Kerr metric field. Using the direction change of vector when it is parallel transported in the metric field of cosmic string, the cone symmetry of the metric field is demonstrated.