[en] In a stationary axisymmetric vacuum gravitational field, the conformal structure of the 3-space is determined by the symmetric, trace free and divergence-less tensor Y/sub ik/. Using the Killing vector K/sup i/ of the axisymmetry, the conformal potential U can be defined by U/sub ,i/ = epsilon/sub ijk/K/sup j/Y/sup kr/K/sub r/. Conversely, the tensor Y/sub ik/ is given algebraically in terms of the gradient U/sub ,i/ of the conformal potential. An attempt is made here to re-formulate the field equations R/sub lambdaμ/ = 0 in terms of the conformal potential. Introducing the Ernst potential as a complex coordinate, the cylindrical radius can be eliminated from the field equations. (author)