Hello. Your photos is an Indian Fantail. The 'normal' fantail pigeon comes in various types.... the show quality kind and the 'garden variety'. The show kind, as you know, has its head tucked back to the base of the fanned tail.. and its chest puffed right out in front... it will stand on it's tip toes to keep balance. To my they look really ugly and deformed.. and I don't think they can have much quality of life like that... must get bad backache lol.
The Garden variety is much less extreme. These are the kind that people in the UK keep in garden dove cotes. They still have the fan tail.. held upright, but their neck and head are in the more normal position.. straight up, and they don't tuck the head far back like the show ones. They are funny as most will wobble their heads and necks back and forth when excited, which is very cute. They are good flyers too.... as far as they can spot predators are able to fly strongly up to a safe high up perch. However, they don't fly up in the air for long like homers, they just fly from A to B.
