Diagram of a Kopesh Sword
The earliest records of a forward curved sword can be traced back to the 3rd millennium BCE Sumer Civilization in Mesopotamia, the earliest civilization in the ancient Near East. The name of this sword is a Egyptian word for the Caananite sickle sword, Kopesh. The ancient hopesh had a hilt of about 18 cm with a 40 cm long blade. The blade then curved into a cresent shape for another 15-30 cm, the edge located on the outer side. This forward curved sword is regarded as the forefather of all forward curving blades.
The Egyptians came into contact with the Kopesh through warfare. They adopted this forward curving sword which gained popularity during the New Kingdom (16th-11th century BCE) and was used by Ramses II (ca.1303 BCE-1213 BCE) the first pharaoh to use in warfare.
Curved swords appear frequently in Mesopotamian art as symbols of authority, often in the hands of gods and kings.
There are some records which indicate that in the 19th century the ancient Egyptians had contact with the Indian sub-continent, under pharaoh Sesostris, and perhaps even invaded certain parts although this is dismissed by most scholars. There is very little scholarly work that suggests a relationship between the Sumer, Egyptians and the Indian sub-continent. What is clear is that the Indo-Aryan migration took place between 2000-1500 BCE bringing a new ethnic group to the Indian sub-continent, with a new culture and religion.
In this way, the very effective forward curved sword entered history and spawned numerous variations across a broad geographic area.
See: Curved Blades
For a discussion of the Kopesh, look here.