本文利用高度函数给出了旗流形U(n)/U(n-k)* T^{k}和 Sp(n)/Sp(n-k)* T^{k}上同调环的自同态映射，计算了相应的Lefschetz数。 用同样的方法可以得到SO(2n+1)/SO(2n-2k+1*T^{k}以及SO(2n)/SO(2n-2k)* T^{k}上同调环的自同态映射及其Lefschetz数。对于Sp(n)/U(k)*Sp(n-k)上同调环的自同态做了初步探索。第一章介绍研究背景和本文的主要结论，第二章具体计算上述几个旗流形的上同调环，第三章是主要结果的计算过程，最后一章是对Sp(n)/U(k)*Sp(n-k)上同调环的自同态的尝试计算。

In this paper, the cohomology endomorphisms of the flag manifoldsU(n)/U(n-k)*T^{k} , Sp(n)/Sp(n-k)* T^{k},SO(2n+1)/SO(2n-2k+1)* T^{k}and SO(2n)/SO(2n-2k)* T^{k}are computed ,the Lefschetz numbers of these cohomology endomorphisms are also computed . At the same time, for the cohomology of Sp(n)/U(k)* Sp(n-k), we try to consider the same problem. Chapter One is the background and main results of this paper. In Chapter Two,the cohomology endomorphisms of the above flag manifolds are computed. Chapter Three gives the proof of the main results. In Chapter Four, we try to compute the cohomology endomorphism ofSp(n)/U(k)*Sp(n-k).