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We examine the separability properties of the equation of motion for astationary string near a rotating charged black hole with two independentangular momenta in five-dimensional minimal gauged supergravity. It is knownthat the separability problem for the stationary string in a general stationaryspacetime is reduced to that for the usual Hamilton-Jacobi equation forgeodesics of its quotient space with one dimension fewer. Using this fact, weshow that the "effective metric" of the quotient space does not allow thecomplete separability for the Hamilton-Jacobi equation, albeit such aseparability occurs in the original spacetime of the black hole. We also showthat only for two special cases of interest the Hamilton-Jacobi equation admitsthe complete separation of variables and therefore the integrability for thestationary string motion in the original background: namely, when the blackhole has zero electric charge or it has an arbitrary electric charge, but twoequal angular momenta. We give the explicit expressions for the Killing tensorscorresponding to these cases. However, for the general black hole spacetime theeffective metric of the quotient space admits a conformal Killing tensor. Weconstruct the explicit expression for this tensor.

Stationary Strings in the Spacetime of Rotating Black Holes in Five-Dimensional Minimal Gauged Supergravity