Tt* geometry of rank two

Abstract

A notion of a Frobenius manifold with a nice real structure was introduced by Hertling. It is called CDV structure (Cecotti-Dubrovin-Vafa structure). In this paper, we introduce a “positivity condition” on CDV structures and show that any Frobenius manifold of rank two with real dimension can be equipped with a positive CDV structure. We extend naturally the symmetries of Frobenius structures given by Dubrovin to symmetries of CDV structures, which will play an important role.