  The N=4 gauged SU(2)$\times$SU(1,1) supergravity in four-dimensional
Euclidean space is obtained via a consistent dimensional reduction of the N=1,
D=10 supergravity on $S^3\times AdS_3$. The dilaton potential in the theory is
proportional to the difference of the two gauge coupling constants, which is
due to the opposite signs of the curvatures of $S^3$ and $AdS_3$. As a result,
the potential can be positive, negative, or zero-depending on the values of the
constants. A consistent reduction of the fermion supersymmetry transformations
is performed at the linearized level, and special attention is paid to the
Euclidean Majorana condition. A further reduction of the D=4 theory is
considered to the static, purely magnetic sector, where the vacuum solutions
are studied. The Bogomol'nyi equations are derived and their essentially
non-Abelian monopole-type and sphaleron-type solutions are presented. Any
solution in the theory can be uplifted to become a vacuum of string or
M-theory.
