# On adding a variable to a Frobenius manifold and generalizations

@article{David2012OnAA, title={On adding a variable to a Frobenius manifold and generalizations}, author={Liana David}, journal={Geometriae Dedicata}, year={2012}, volume={167}, pages={189-214} }

Let $$\pi :V\rightarrow M$$ be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure $$(\circ _{M},e_{M},g_{M})$$ and typical fiber has the structure of a Frobenius algebra $$(\circ _{V},e_{V},g_{V})$$. Using a connection $$D$$ on the bundle $$\pi : V{\,\rightarrow \,}M$$ and a morphism $$\alpha :V\rightarrow TM$$, we construct an almost Frobenius structure $$(\circ , e_{V},g)$$ on the manifold $$V$$ and we study when it is Frobenius. In particular, we describe all…

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