It starts off with a guy walking to college or something and a girl that either jumped or was pushed off a high roof lands on him, killing them both.
They then meet god together and he says that they have to live with each other for one week or so. And in that time they can't be separated from each other because they can feel each others feelings. And at the end of the week one of them has to die.
At first they don't really like each other, but they gradually fall in love. At one point they go to the girls mothers grave on a cliff side. They then try to commit suicide together. But then they just come back alive.
I also remeber that the guy quite liked drawing.
But in the end the guy ends up volunteering to die. And I think the girl ended up having a kid with him before he died aswell.
If you could tell me this mangas name, that would be awesome.