There are a number of things that could answer this question. A few answers are:
Knife
Scalpel
Saw
Razor
your but
Machete
A padsaw is a type of narrow-bladed saw used especially for cutting curves.
You are probably refering to a meat cleaver.
A sickle is a tool use to cut grass or grain. Flint bladed means that it uses sharp chips of flint rock for the cutting edges.
a saw
A bistoury is a narrow-bladed surgical knife.
A circular saw is probably not a good tool for cutting curly (or any other kind of) hair. You might want to narrow your question down a bit.
A shovel...?
A jigsaw is a hand held electrical tool with a narrow saw blade, used for cutting timber, the narrow blade allows the cut to turn corners, or cut intricate pattern's
A steel bladed knife will hold a sharp cutting edge.
The Renaissance fencing sword was a narrowed bladed sword called a 'Rapier'.