why people don't use the same generators? i want to make many pederson commitments $C=g^s h^r$ for a long time , do i have to change the generators $g$ and $h$ or its ok if i always used the same ones
You can use the same $g$. However, if the discrete log of $h$ relative to $g$ is known, then Pedersen is no longer binding. Thus, you cannot use an $h$ if there is any possibility of someone else knowing that discrete log.