中文摘要：

将欧式空间中经典的Brouwer不动点定理推广到了Heisenberg群Hn上，主要定理可叙述为：设f：BH→BH∩Hξ是光滑映射，则f在BH∩Hξ中必有不动点，其中BH为Hn中的单位闭球，Hξ是过ξ∈BH的水平平面。

英文摘要：

In this paper,the classical Brouwer fixed point theorem in Euclidean space is generalized to the Henberg group Hn.The main result is as follows：If f：BH→BH∩Hξ is a smooth mapping,there exists a fixed point in BH∩Hξ,where Bn is a Koranyi unit closed ball,and Hξ is a horizontal plane through a point ξ∈BH.