Arching of the back
 

Hello, what is the purpose of the arching of the back?
Beside a slight increasing of volume of the resonance body.
If you take a guitar with a heavily arched back in both directions and compare it to one built in the exatly same manner and materials, what would the difference be in comparison to one with a completely flat back?

Added strength. An arched shape is more resistant to deformation than a flat one. Increases, somewhat, crack resistance since, when shrinking , it can flatten, whereas a flat back has no where to shrink. Theory is that a back not parallel to the top alters sound waves in the body.

Yeah, good point. Guild has famously and successfully made arch-back guitars for many years, and they generally sound fabulous (despite the backs being laminate). Not only are the backs arched, they're braceless, which I think makes a big difference, too.

I agree with Charles, except I believe it's more for resistance to cracking, the increase in strength is not that significant. The exception to that is the Larsen Brothers design of a 12' cylindrical radius for the top, which would be much stiffer longitudinally than the typical 20'+ spherical radius. Which is more important is not really a point worth debating.

My Taylor BBT has an arched, laminated back which is strong enough that the back needs no internal bracing. Lightens the guitar up, which is a good thing for a travel guitar.

Braceless arched backs, whether laminate or carved, work differently than braced ones. In essence, they are using arch height and plate thickness to get the stiffness that a 'flat' back gets from bracing. There are advantages and disadvantages to each system, in terms of acoustics, strength, material costs and the time required to make them.