Mahayana Buddhism developed in South India, while Hinayana (Theravada) Buddhism developed in Sri Lanka. Bhodidharma who is supposedly from West South India (or what is today the state of Kerala) transmitted "Chaan" Buddhism to China. Has a lot to do with the Lankavatara Sutra, which is supposed to have taken place in Sri Lanka between the Buddha and a Bodhisattva named Mahamati "Great Wisdom". Zen Buddhism was fully developed by the time it was exported to China and then from China, to Japan. In those nations, Zen Buddhism became further refined within their cultures. Bodhidharma's teacher was Prajnatara. She was an ordained Buddhist Nun of the Sarvastivada Sect of Buddhism. Also the Indian Monk Paramartha (from Ujjain) stayed in the Chinese Emperors court of Wu of Liang and was one of the most prolific translators of Buddhist texts to Chinese texts. He was called "Chen Ti" in China Buddhism, in all its forms, died in India due to various reasons. In South India, it died of neglect and Hindu intolerance. Mahayana Buddhism became an expression of China. Vajrayana Buddhist (Thunderbolt) became an expression of Tibet, This form unites Buddhism and Hindu Tantra, so you have icons of the Buddha and Goddess Tara together in Nepalese Bronzes. The Lankavatara Sutra describes the various tiers of consciousness in the individual. This Sutra culminates in the Thathagathagarba Sutra (The Buddha Matrix, the Buddha-Embryo, The Buddha-essence lit, the womb of the thus- come-one) within all sentient creatures. It is the indwelling Buddha. Generally speaking unlike Christianity which came to Europe in its infancy and then grew up in Europe Buddhism stayed in India for 200 years before Sri Lanka was converted in 300 BC. China adopted Buddhism around 200 AD ( 900 years after it was born -500 BC) and Japan adopted Buddhism in 600 AD (1100 years later). Chinese Emperors had cartloads of Sanskrit and Pali scripts brought from India's Buddhist centers and Universities (Nalanda, Vikramashila Taxila) to China. One of the earliest Buddhist Sutras is the Kalama Sutra which teaches people how to think in order to learn. How to discern dogma from philosophy.