论文标题
通过本质上的谐波形式对n维圆环的表征
A characterization of the n-dimensional torus via intrinsically harmonic forms
论文作者
论文摘要
$ n $ -torus是唯一的封闭流形，支持一组$ n $ linearly独立的封闭$ 1 $ - 形式。在本文中，我们对此结果进行了改进，并表明圆环是独特的封闭$ n $二维流形，支持线性独立的集合，该套件由$（n-1）$封闭$ 1 $ forms组成，其产品决定了非零同类群。
The $n$-torus is the the unique closed manifold supporting a set of $n$ linearly independent closed $1$-forms. In this paper we improve on this result and show that the torus is the unique closed $n$-dimensional manifold supporting a linearly independent set consisting of $(n-1)$ closed $1$-forms whose product determines a non-zero cohomological class.
