Gated communities in South Delhi

We are considering moving to Delhi from the US and are looking to live in South Delhi and would like to live in a gated community/society. We have young kids and think a gated community will be a good fit as all amenities (pool, play area, gym) and classes will happen in the community, and it will be easier for the kids to meet other kids and make friends. We really enjoy being close to culturally rich areas so we can go to concerts, theatre and performing arts etc hence the desire to live in south or central Delhi. Are there any communities/societies like this in or close to South Delhi? Thanks in advance! Please note: not looking for advice on whether to move to Delhi from the US.