How do you install carpet in a curved area?
I want to put tile flooring coming in my front door,This tile will be curved after 4 rows. Carpet than will be installed. How do I install the curved portion of the carpet as I can’t use tack strips?Do I fold it over and tack it similar to step runner installation? Do I glue it? If so, what type of glue? Other better methods?

To match carpet to a flat curved surface, you can use metal edging like you would often see at a doorway, except in a version called Contour carpet bar. The tacks are built in. It’s like straight carpet bar edging except the lower bar with the tacks is slotted. This allows the bar to be curved as needed.
You can also do this with tackstrip by cutting the strips to the length needed to keep the gap between the strip and curve between 3/8 and 3/4".
A third way uses no tackstrip, it’s called turn & tack. You cut the pad about 1-1/4" short of the curve, and the carpet about 1" long. The carpet is then folded under and tacked down through the face while being stretched to the curve, with the knee kicker used to maintain pressure.
The contour metal is the easiest to do if you aren’t experienced.
Why can’t you use tack strips? they are just cut down into smaller sections to form the arc of your circle/radius
there are two options. It used to be that carpet installers would always install tap down flex metal. The flex metal has pins (teeth) to hold the carpet in place, yet has cut in the underside to allow it to bend and flex into the desired shape. Most installers these days do not use the metal, but turn the carpet under itelf and tack it down. Tack Strips can also be used, but these must be cut into small pieces, to allow for the curve.