利用中心投影的思想证明了一类~$n+1$~次平面拟齐次向量场的几何性质仅依赖于它的诱导向量场.并根据其诱导向量场的性质证明了该向量场有10种不同拓扑结构的扇形不变区域,进而讨论了其全局拓扑结构,得到了该向量场当~$n$~为偶数时有~13~种不同的全局拓扑等价类,当~$n$~为奇数时有~12~种不同的全局拓扑等价类.

In this paper, by using the idea of the central projection it is shown that the geometric property of a class of planar quasi-homogeneous  vector fields of degree $n+1$  depends on their induced vector fields.  By virtue of its induced vector field, it is proven that this vector field  has 10 types of sector invariant fields with different topological   classification. Furthermore, its global topological structure is  discussed and it is shown that there are 13 types of different topological classification when $n$  is even number and 12 types of different   topological classification when  $n$  is odd number.