标题： 由向量场诱导的$1$-可微上同调 显示英文标题

标题： An $1$-differentiable cohomology induced by a vector field

摘要： 一种由向量场引起的新的上同调，在流形上的微分形式对（$1$—可微形式）上被定义。 证明了与经典de Rham上同调以及与一个1-形式相关的Lichnerowicz型$1$—可微上同调之间的联系。 此外，研究了当流形是复流形且向量场是全纯的情况。 最后，研究了该理论在特定情况下$1$—可微形式的调和性中的应用。 显示英文摘要

摘要： A new cohomology, induced by a vector field, is defined on pairs of differential forms ($1$--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an $1$-differentable cohomology of Lichnerowicz type associated to an one form. Also, the case when the manifold is complex and the vector field is holomorphic is studied. Finally, an application of this theory to the harmonicity of $1$-differentiable forms is studied in a particular case.