  A new class of non-compact Kahler backgrounds accompanied by a non-constant
dilaton field is constructed as a supergravity solution. It is interpreted as a
complex line bundle over a base manifold comprising of a combination of
arbitrary coset spaces, and also includes the case of Calabi-Yau manifolds. The
resulting backgrounds have U(1) isometry. We consider N=2 supersymmetric
sigma-models on them, and derive a non-Kahlerian solution by U(1) duality
transformation, which preserves N=2 supersymmetry.
