On the calculation of the special geometry for a Calabi–Yau loop manifold and two constructions of the mirror manifold

The Kähler potentials have been calculated on the moduli space of complex structures for two Calabi–Yau manifolds specified as hypersurfaces in weighted projective spaces. Mirror images of these manifolds have been found according to the Batyrev and Berglund–Hübsch constructions and their equivalence has been demonstrated.