Multiplication on the tangent bundle

1999/10/21 by Claus Hertling, Hertling, Claus
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math.AG #math.QA #math.SG

paper · pdf · doi:10.48550/arxiv.math/9910116

88 pages, AMS-LaTeX

arxiv created 1999/10/21 · arxiv updated 2009/11/30

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.

Related

• Manifolds with multiplication on the tangent sheaf
• F‐Manifolds and geometry of information
• Linear F-manifolds, a duality and the generalized tangent bundle
• F-manifolds with flat structure and Dubrovin's duality
• Frobenius manifolds and algebraic integrability