Traditionally, a katana does have a gentle curve along its blade. The curvature, known as the "sori" in Japanese, is a distinctive feature of the katana and contributes to its functionality and aesthetic appeal.

The curve in a katana serves several purposes. Firstly, it enables the cutting edge of the blade to have a longer contact area with the target during a slashing or cutting motion, enhancing its cutting efficiency. The curve allows for smoother, more fluid cutting techniques.

Secondly, the curvature aids in the draw and sheathing of the katana from its scabbard (saya). The curve allows for a smooth, controlled motion when unsheathing the blade and facilitates swift and fluid movements during combat.

However, it's important to note that not all swords referred to as "katana" necessarily have the same degree of curvature. While a gentle curve is characteristic of the traditional katana, there can be variations in the degree of curvature depending on the specific design, regional styles, and personal preferences of the swordsmith.

In modern times, there are also straight-bladed swords that resemble katana but are not considered true katana due to their lack of curvature. These straight-bladed variations are often referred to as "chokuto" or "tachi" swords, which have a historical significance and precede the development of the curved katana.

In summary, while the traditional katana is known for its gentle curve, there can be variations in the degree of curvature based on design, regional styles, and personal preferences. The curvature contributes to the functionality and distinctive aesthetic of the katana, but it's not an absolute requirement for a sword to be called a katana.