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Abstract
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We consider a string model at one-loop related to a -model whose antisymmetric tensor
field is constructed as complex structure on the background manifold, especially on a
manifold R × N where N is a complex manifold. As an example, we consider a homogeneous
anisotropic (1 + 4)-dimensional -model where space part of the background
is a four-dimensional complex manifold. By solving the related one-loop -functions,
we obtain a static solution so that by reduction of this solution to (1 + 3)-dimension,
we obtain a static solution of Einstein equation where the matter sector is effectively
interpreted as an inhomogeneous, anisotropic and barotropic matter satisfying all the
energy conditions. Finally, the T-dual background of the solution is investigated and it
is shown that the duality transformation and reduction processes commute with each
other.
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