Yes, the hilt of a traditional katana typically has a curved shape. The curve in the hilt, known as the "tsuka," is designed to fit comfortably in the hand and provide a secure grip while wielding the sword.

The tsuka of a katana consists of several components, including a wooden handle wrapped in a grip material (often ray skin) and covered with a tightly wrapped cord called the "tsuka-ito." The shape of the tsuka is slightly curved to conform to the natural shape of the hand and allow for better control and maneuverability during combat.

The curvature of the tsuka also complements the overall design and aesthetic of the katana. It harmonizes with the curved blade (known as the "nagasa") and helps maintain a balanced and visually pleasing appearance.

It's important to note that while the hilt of a traditional katana is generally curved, the degree of curvature can vary depending on the specific style, era, or personal preferences of the swordsmith or owner. Different schools of sword-making and individual craftsmen may have slight variations in the curvature of the tsuka, bu