As Boonen stated, the angkes are much steeper (74-75^O) for both head and seat angles are not unusual. There is minimal offset in the forks, which combined with short chainstays gives a very short wheelbase.
The velodrome where I used to ride didn't allow fixed roadbikes because they where afraid of people crashing etc. not really sury why they would, but they didn't allow it.
Track bikes have higher BBs than road bikes and converted road bikes can have their pedals strike the banking causing a fall. In my IP bike I cant ride it on a banked track at under 35-40km/h. The BB is very low and I strike the pedal if I ride too slow.
When you go this way make sure you have a lockring on your rearwheel, the forces on the cog are pretty big and you don't want to have the cog unwind itself!
I have only had a cog unwind once (never use a lock ring) and it was when I was riding the track bike on the road and I was hopping the wheel backwards to slow me down on a hill. I just do a standing start on it as soon as its on.