Superstring compactification and Frobenius manifold structures
For finding Effective Lagrangian which appears after the compactification of Superstring theory on a Calabi-Yau (CY) manifold we need to know the so called Special Kahler geometry on the Moduli space of the CY manifold. We present a simple way for computing the Special Kahler metric. This method uses the fact that the Moduli space is a subspace of the Frobenius manifold connected with the given CY manifold. Due to this fact we are able to calculate two special basises of periods of the CY holomorphic 3-form. The knowledge of these basises together with the holomorphic metric on the Frobenius manifold makes it possible finding the exact expression for Kahler metric on the Moduli space.