A sword with a curved blade is commonly referred to as a "curved sword" or a "saber." The term "saber" specifically denotes a type of curved sword that is often associated with cavalry and military use.

Curved swords are designed with a blade that features a gentle or pronounced curve along its length. The curve can be slight, as seen in some European arming swords, or more pronounced, as seen in Middle Eastern scimitars or Japanese katana. The curvature of the blade enhances the sword's cutting and slashing capabilities, allowing for efficient slicing motions.

In addition to sabers, there are several other types of curved swords found throughout history and various cultures. Some examples include:

1. Scimitar: A scimitar is a curved sword primarily associated with Middle Eastern and North African cultures. It typically has a single-edged blade that curves forward, with a distinctive broad tip.
2. Kilij: The kilij is a curved sword with roots in the Ottoman Empire and Central Asia. It has a curved, single-edged blade that tapers to a point and often features a distinctive yelman (ridge) along the spine.
3. Katana: The katana is a traditional Japanese sword with a curved, single-edged blade. It is known for its exceptional craftsmanship, sharpness, and cutting ability. The curvature of the katana's blade contributes to its unique cutting technique and balance.

These are just a few examples of curved swords found in different cultures and historical periods. The specific design, construction, and terminology of a curved sword can vary depending on its cultural and historical context.