A (TE)-structure \(\nabla \) over a complex manifold M is a meromorphic connection defined on a holomorphic vector bundle over \({\mathbb {C}}\times M\), with poles of Poincaré rank one along \(\{ 0 \} \times M\). Under a mild additional condition (the so-called unfolding condition), \(\nabla \) induces a multiplication on TM and a vector field on M (the Euler field), which make M into an F-manifold with Euler field. By taking the pullbacks of \(\nabla \) under the inclusions \(\{ z\} \times M \rightarrow {\mathbb {C}}\times M\)\((z\in \mathbb {C}^*)\), we obtain a family of flat connections on vector bundles over M, parameterized by \(z\in {\mathbb {C}}^{*}\). The properties of such a family of connections give rise to the notion of (T)-structure. Therefore, any (TE)-structure underlies a (T)-structure, but the converse is not true. The unfolding condition can be defined also for (T)-structures. A (T)-structure with the unfolding condition induces on its parameter space the structure of an F-manifold (without Euler field). After a brief review on the theory of (T)- and (TE)-structures, we determine normal forms for the equivalence classes, under formal isomorphisms, of (T)-structures which induce a given irreducible germ of two-dimensional F-manifolds.

复流形M上的（TE）结构\（\ nabla \）是在\（{\ mathbb {C}} \ times M \}上的全纯矢量束上定义的亚纯连接，庞加莱的极点沿着\（\ {0 \} \ times M \）。在适度的附加条件下（所谓的展开条件），\（\ nabla \）在TM上引起乘法，在M上引起矢量场（欧拉场），这使M成为具有Euler场的F流形。通过在\（\ {z \} \ times M \ rightarrow {\ mathbb {C}} \ times M \）下包含\（\ nabla \）的回调\（（z \ in \ mathbb {C} ^ *）\）中，我们在M上的矢量束上获得了一组平面连接，其参数由\（z \ in {\ mathbb {C}} ^ {*} \参数化。这种连接族的性质引起了（T）-结构的概念。因此，任何（TE）结构都在（T）结构的基础上，但是反之则不成立。展开条件也可以针对（T）结构来定义。具有展开条件的（T）结构在其参数空间上诱导F流形的结构（无欧拉场）。在简要回顾了（T）-和（TE）-结构，我们在（T）-结构的形式同构下确定等价类的正规形式，这些形式诱导给定的不可约二维F-流形细菌。