the problem says that if $m$ is a smooth complete embedded self-shrinker with polynomial volume growth in euclidean space and the squared norm of the second fundamental form $|a|^2 =$ constant, then $m$ is a generalized cylinder. it has been verified in dimension 2 without the assumption of polynomial volume growth. cao and li had proved if $m$ is an n-dimensional complete self-shrinker with polynomial volume growth in $r^n+q$, and if $|a|^2 \leq 1$, then $m$ is must be one of the generalize cylinders. but for the case $|a|^2 >1$, they don't know what it is. therefore, qingming cheng and guoxin wei proved if the squared norm of the second fundamental form $|a|^2$ is constant and $|a|^2 \leq 10/7$, then $m$ is must be one of the generalize cylinders. so we guess that it may be true if the squared norm of the second fundamental form $|a|^2$ is constant.