Can the residential property management company build a bicycle parking shed on the public green space of the residential area?

You can't. Green space belongs to the public * * * setting, and the property right belongs to all owners. If it is really necessary to build a bicycle parking shed in the community, it can be built without affecting the public facilities. If it is really necessary to destroy the public facilities, a meeting of the owners' committee shall be held, and the construction can be implemented only after the consent of the owners' committee.