Concave (curves inward) arrays limit the sweet spot listening area and in fact become one or two rows of listeners deep if your are close to their focal point. In the limit you have a one listener in the sweet spot. In reality the drivers are directed to overlap essentially the same volume in space so you attain none of the advantages of near field arrays that I have stated.
On the other hand concave curved arrays (curved outward typically in a J-shaped curve) are widely used in the pro sound field. The goal for the convex curved arrays is to blend their near and far fields so that the sound quality is improved for additional listeners within the audience.
Bottom line is that concave arrays limit the listening space while convex arrays expand the listening space.
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