1201.0948 (Liana David)

On adding a variable to a Frobenius manifold and generalizations    [PDF]

Liana David

Let \pi : V \rightarrow M be a (real or complex) vector bundle whose base is a Frobenius manifold and typical fiber a Frobenius algebra. Using a connection D on the bundle V and a morphism \alpha : V \rightarrow TM, we construct an almost Frobenius structure on the manifold V and we study when it is Frobenius. We describe all (real) positive-definite Frobenius structures on V obtained in this way, when M is semisimple with non-vanishing rotation coefficients. We study in detail a class of Frobenius structures on the product M\times \mathbb{K}^{r} obtained by our method. Along the way, we prove various properties of adding variables to a Frobenius manifold, in connection with Legendre transformations and tt*-geometry.

View original: http://arxiv.org/abs/1201.0948