Multiplication on the tangent bundle

Abstract

Manifolds with a commutative and associative multiplication on the tangent bundle are called F-manifolds if a unit field exists and the multiplication satisfies a natural integrability condition. They are studied here. They are closely related to discriminants and Lagrange maps. Frobenius manifolds are F-manifolds. As an application a conjecture of Dubrovin on Frobenius manifolds and Coxeter groups is proved.

88 pages, AMS-LaTeX

References in corpus (1)

• Differential geometry of the space of orbits of a Coxeter group

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