  It has been known for some time that the SL(2,R) WZWN model reduces to
Liouville theory. Here we give a direct and physical derivation of this result
based on the classical string equations of motion and the proper string size.
This allows us to extract precisely the physical effects of the metric and
antisymmetric tensor, respectively, on the {\it exact} string dynamics in the
SL(2,R) background. The general solution to the proper string size is also
found. We show that the antisymmetric tensor (corresponding to conformal
invariance) generally gives rise to repulsion, and it precisely cancels the
dominant attractive term arising from the metric.
  Both the sinh-Gordon and the cosh-Gordon sectors of the string dynamics in
non-conformally invariant AdS spacetime reduce here to the Liouville equation
(with different signs of the potential), while the original Liouville sector
reduces to the free wave equation. Only the very large classical string size is
affected by the torsion. Medium and small size string behaviours are unchanged.
  We also find illustrative classes of string solutions in the SL(2,R)
background: dynamical closed as well as stationary open spiralling strings, for
which the effect of torsion is somewhat like the effect of rotation in the
metric. Similarly, the string solutions in the 2+1 BH-AdS background with
torsion and angular momentum are fully analyzed.
