Frobenius manifolds and algebraic integrability

Abstract

We give a short review of Frobenius manifolds and algebraic integrability and study their intersection. The simplest case is the relation between the Frobenius manifold of simple singularities, which is almost dual to the integrable open Toda chain. New types of manifolds called extra special Kaehler and special F-manifolds are introduced which capture the intersection.

18 pages, 1 figure, to appear in Encyclopedia of Peyresq (2007)

References in corpus (2)

• Solutions of WDVV equations in Seiberg-Witten theory from root systems
• Geometric transitions and integrable systems