"obsession about" is correct and usable in written English.
You can use it to indicate an intense preoccupation with something. For example, "She had an obsessive about collecting stamps."
The obsession about styles came later".
"What's with all this obsession about the war?" I asked.
He show signs of mild obsession about playing golf.
"Some would say we have an obsession about it".
In the end, China may have a point with its obsession about economics.
And he has something close to an obsession about making the middle seat more comfortable.
The obsession about tanning and the gym has led to parodies on YouTube.
This stoked an obsession about conspiracy theories fueled by his mother's many books on the assassination.
And with Papaji on the mend, my sudden obsession about having children is fading too.
But there is less of an "obsession" about that these days, he said, "because they're making their own media".
He said: "This obsession about putting work out into the cinema can distract from making amazing quality work.
