${\bf R}^n$上$k$-型的分类及流形上相伴几何的存在性
Classification of $k$-forms on ${\bf R}^n$ and the existence of associated geometry on manifolds
摘要：
本文综述了$k$-形式的分类方法和结果（分别是：$k$-${\bf R}^n$上的向量），理解为标准${\bf GL}(n, {\bf R})$的轨道空间的描述-对$Λ^k {\bf R}^{n*}$的作用（分别为在$Λ^k {\bf R}^n$上）。讨论了光滑流形上由微分形式定义的相关几何的存在性。本文还包含一个附录米哈伊尔Borovoi伽罗瓦上同调方法寻找真正的形式复杂的轨道。
英文摘要：
In this paper we survey methods and results of classification of $k$-forms (resp. $k$-vectors on ${\bf R}^n$), understood as description of the orbit space of the standard ${\bf GL}(n, {\bf R})$-action on $Λ^k {\bf R}^{n*}$ (resp. on $Λ^k {\bf R}^n$). We discuss the existence of related geometry defined by differential forms on smooth manifolds. This paper also contains an Appendix by Mikhail Borovoi on Galois cohomology methods for finding real forms of complex orbits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
