In Japan you don't keep eye contact, in Korea (and China too I think) you do. The reason you do not keep eye contact is because you're expressing trust for that person, trust that you can take your eyes off of him and he won't kill you. If you keep eye contact it means you don't trust him.
Now the prez could have kept his back straight, that would be a proper Japanese bow.
I have no problem with bowing to the leader of a nation for which bowing is appropriate, such as Japan, China, Korea, etc. Bowing before the king of England is wrong. Bowing before anyone who does not bow back is wrong. Bowing lower than someone makes you not an equal, and is thus wrong.
Now the prez could have kept his back straight, that would be a proper Japanese bow.
I have no problem with bowing to the leader of a nation for which bowing is appropriate, such as Japan, China, Korea, etc. Bowing before the king of England is wrong. Bowing before anyone who does not bow back is wrong. Bowing lower than someone makes you not an equal, and is thus wrong.