  At the leading order, the low-energy effective field equations in string
theory admit solutions of the form of products of Minkowski spacetime and a
Ricci-flat Calabi-Yau space. The equations of motion receive corrections at
higher orders in \alpha', which imply that the Ricci-flat Calabi-Yau space is
modified. In an appropriate choice of scheme, the Calabi-Yau space remains
Kahler, but is no longer Ricci-flat. We discuss the nature of these corrections
at order {\alpha'}^3, and consider the deformations of all the known
cohomogeneity one non-compact Kahler metrics in six and eight dimensions. We do
this by deriving the first-order equations associated with the modified
Killing-spinor conditions, and we thereby obtain the modified supersymmetric
solutions. We also give a detailed discussion of the boundary terms for the
Euler complex in six and eight dimensions, and apply the results to all the
cohomogeneity one examples.
