Identification of Two Frobenius Manifolds In Mirror Symmetry

Abstract

We identify two Frobenius manifolds obtained from two different differential Gerstenhaber-Batalin-Vilkovisky algebras on a compact Kaehler manifold. One is constructed on the Dolbeault cohomology, and the other on the de Rham cohomology. Our result can be considered as a generalization of the identification of the Dolbeault cohomology ring with the complexified de Rham cohomology ring on a Kaehler manifold.