Track
Track bikes are all about rigidity and responsiveness, they do not have to have and importance given to comfort as they are designed purely for use on the velodrome.
There is not usually any real benefit in most cases to be gained from using carbon fibre frames, the main benefits of carbon on a track bike is either to create an aerodynamic frame whilst still retaining a low weight and adequate rigidity, or for a sprint frame where a frame can be built to be ultra rigid whilst being a reasonable weight.
There are very few titanium track frames, most tend to be aluminium, aluminium and carbon, steel, or full carbon.
track bikes do not have brakes or gears consequently the frames are designed with this in mind, although a lot of the lower end models may well have facilities for a front brake so they may be used on the road, bottom bracket heights tend to be higher so that the pedals clear the track on the bankings, the head angles tend to be steeper to sharpen up the steering making the steering livelier and quicker to change direction.