I am going to assume here that you will use the curved section between the two columns as a straight line, to introduce simplification. Otherwise, there might be chance for the whole ring to topple.
Well, it depends on how are you placing the ring on top of the columns. Are you gluing/welding the ring ontop of the columns, or just placing it over them? Because if you are gluing/welding it to the top of columns, then these can be thought of as fixed supports. But if you are just placing, then it becomes a bit more complicated.
Considering the case you are gluing/welding them ontop of the columns, then you may refer to the link below to calculate the displacements within that region of the ring which is lying between the two columns. The rest of the ring can be assumed to not experience any deflection.
How to calculate Deflection of a beam fixed at both ends
Now, when you consider that you are just placing the ring ontop of the columns, then both of the ends can be assumed as pinned supports. A pinned support means that the ring at the supports cannot move in perpendicular or sideways directions, but can rotate at that point. (You may further research about what pinned supports are). There is an assumption here that the ring at the support cannot also move in the perpendicular up direction (although it can in the figure as you shared). Another assumption is that it cannot move sideways because after coming into static equilibrium, it will not be possible for the ring to move sideways. However, in this case, the rest of the part of ring i.e. which is not in the region between the two columns will also experience deflection.
How to calculate Deflection of a beam pinned at both ends