The reason why the rainbow is curved is that all the angles of the water drop have to be just right for the drop to send some sunlight to you, standing on the ground. So, with the sun behind you, only those water droplets that have the same angle formed by you, the drop, and the sun (this angle happens to be approximately 42 degrees) will contribute to the rainbow. Other droplets send their light somewhere else, and if you move to a different location, new droplets are needed to make the rainbow you see in the new location.