Those of us not involved with leatherworking may have never seen this tool:
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Those are called swivel knives. The user rests a finger in the curved saddle up top to provide downward pressure, and the rest of the tool swivels between the thumb and other fingers, allowing the user to change direction.
Although the edge is chisel-tipped, it is not used like a woodworking chisel, whereby the width of the blade corresponds with the width of the cut; instead the user slices with it, and by using just the corner of the blade, can make what appear to be impossibly tight curves. To see what I mean, take a look at this close-up footage of master leatherworker/saddlemaker Bruce Cheaney demonstrating some test cuts:
Although that video has "how to" in the title, there isn't much in the way of instruction. If you'd like to see a more in-depth tutorial on how to master this thing, here another master leatherworker/saddlemaker, Don Gonzales, delivers: