Actually, I have an identical problem. After less than a month of use, I noticed that my ipad air was bent. I noticed during the day while I was using it to play XCOM Enemy Unknown that it was too hot to touch with my bare hands. Shortly after that I put it in a bag with some other things for a couple of hours. I didn't step or sit on it, I didn't apply any great pressure to the bag at all, the only pressure was a mild pressure of some clothes pressed up against it inside the bag. But I did take it with me outside for a few minutes where it was around 5 degrees Celsius.
When I took it out later and tried to stand it up using my cover, it didn't stick like it had before. I was shocked to find that the side without the volume buttons was significantly bent towards the middle just like OP's pictures, except that the curve is in the direction of the glass.
I tried getting it to heat up again and pressed the ipad against a table to straighten it out somewhat, but although the corners could be pressed down temporarily, it immediately returned to its new bent form.
Thank you for posting. Now that I know that I'm not alone, I'm tempted to have it looked at. Only problem is there are no apple stores anywhere in my part of Japan. I bought it at a mobile phone service provider for the cellular model and it took 6 weeks to arrive, so I'm worried having it looked at will take over a month (and I use my iPad every day for work), only to be told that they won't take responsibility and fix/replace it.
I've had no performance problems despite the bend, but it really is frustrating to see that slight bend every single time I use it. And to be stuck with it for nearly 2 years just adds insult to injury.
