Some Constraints on Frobenius Manifolds with a TT*-Structure

Details Some Constraints on Frobenius Manifolds with a TT*-Structure Some Constraints on Frobenius Manifolds with a TT*-Structure

2009-04-21

arxiv.org/abs/0904.3219v1

Mathematics

Differential Geometry

Scientific paper

The article gives a necessary and sufficient condition for a Frobenius manifold to be a CDV-structure. We show that there exists a positive definite CDV-structure on any semi-simple Frobenius manifold. We also compare three natural connections on a CDV-structure and conclude that the underlying Hermitian manifold of a non-trivial CDV-structure is not a Kahler manifold. Finally, we compute the harmonic potential of a harmonic Frobenius manifolds.

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