  The dimensional reduction of the bosonic sector of five-dimensional minimal
supergravity to a Lorentzian four-dimensional spacetime leads to a theory with
a massless axion and a dilaton coupled to gravity and two U(1) gauge fields and
the dimensionally reduced equations of motion have SL(2,R)/SO(2)-duality
invariance. In our previous work, utilizing the duality invariance, we
formulated solution-generation techniques within five-dimensional minimal
supergravity. In this work, by choosing a timelike Killing vector, we consider
dimensional reduction to a four-dimensional Euclidean space, in which the field
equations have SL(2,R)/SO(1,1) invariance. In the timelike case, we develop a
new duality transformation technique, while in the spacelike case we have done
that in the previous work. As an example, by applying it to the Rasheed
solutions, we obtain rotating Kaluza-Klein black hole solutions in
five-dimensional minimal supergravity. In general, in contrast to the spacelike
case, the resulting dimensionally reduced solution includes the so-called NUT
parameter and therefore from a four-dimensional point of view, such a spacetime
is not asymptotically flat. However, it is shown that in some special cases, it
can describe ordinary Kaluza-Klein black holes.
