T-duality on Almost Hermitian Spaces

We investigate T-duality transformation on an almost bi-hermitian space with torsion. By virtue of the Buscher rule, we completely describe not only the covariant derivative of geometrical objects but also the Nijenhuis tensor. We apply this description to an almost bi-hermitian space with isometry and investigate integrability on its T-dualized one. We find that hermiticity is not a sufficient condition to preserve integrability under T-duality transformations. However, in the presence of the K\"{a}hler condition, the T-dualized space still admits integrability of the almost complex structures. We also observe that the form of H-flux is suitable for string compactification scenarios.