The piece of wood over which the strings are stretched and gripped is the fingerboard.
Lengthways it is slightly hollow and somewhat round laterally. It is made of hard wood. During the Stradivarius age the fingerboard was made with a hardwood veneer only. Nowadays it is always made of solid hardwood, usually ebony. Much more rarely fingerboards are made of palisander.
When viewed from across there is some curvature, the radius being somewhat narrower than the bridge. In the lateral direction it is a bit hollow in order to allow the strings to better vibrate. The hollow is more pronounced where the strings are deeper and where the instrument has a deeper tone because of the greater amplitude for vibration. The length of the board has a width of 5/6th of the vibrating strings length.