中文摘要：

设π：M^n→PN是Pn上的小覆盖，S是P^n的任意一个n-1维截面．给出了π一（S）是n-1维闭子流形（或者两个相互同胚n-1维闭子流形的不交并），以及π^-1（S）是n-1维伪流形的充要条件．

英文摘要：

Let π^ ： Mn →P^n be a small cover of P^n, S an （n- 1） dimensional section of P^n. The author deals with the relationship between S and π^-1 （S）, and obtains a necessary and suKicient condition to guarantee that π-1 （S） is an （n-1） dimensional closed submanifold （or the disjoint union of two （n - 1） dimensional closed submanifolds which are homeomorphic to each other）, and a necessary and sufficient condition to guarantee that π-1（S） is an （n - 1）-dimensional pseudomanifold.