Yb. Wu, DOUBLE HARMONIC-MAPPINGS OF RIEMANNIAN-MANIFOLDS AND ITS APPLICATIONSTO STATIONARY AXISYMMETRICAL GRAVITATIONAL-FIELDS, International journal of theoretical physics, 33(12), 1994, pp. 2415-2427
Harmonic mappings of Riemannian manifolds are discussed by a double co
mplex function method, and the double-complex Ernst equation and the r
elated Backlund transformations are naturally derived. Further, the Er
nst solution and its dual solution are obtained by two different metho
ds, respectively. Therefore, the results obtained by A. Eris are exten
ded to a double form.