Your cat might roll over on their back, belly up when they see you but I am not sure that it is very commonplace. It happens but less often than the classic cat greeting which is to come up to you and rub their flank against your leg and hop up to head butt your hand. They are both scent exchange methods. The belly up is not a scent exchange interaction. The ‘roll over belly up’ greeting is that of a lazy or sleepy cat who deeply trusts their caregiver as they place themselves in a vulnerable position. It must depend, too, on the confidence of the cat. The more confident cat is more likely to do it while the timid cat normally won’t.
Sometimes even feral cats in managed colonies (TNR) will do this (see pic below). And they might also be inviting a belly rub if that routine has been set up over a long time. There is no reason why the belly-up greeting can’t be incorporated into a petting session even on the sensitive stomach. It depends on the relationship and the cat’s sense of confidence. All belly rubs should be very gentle and respectful as we all know.
Below are some more articles on scent exchange which is often incorporated into greetings.
