I have been listening to Dan Carlin's "Hardcore History" podcast, he dedicates five episodes on the conquest of the Khans. Looking at the maps of the Khans conquest, one sees great expansion into China, much of greater Asia, and the Middle East. Except for India. Why?
I don't have the exact page number on hand, but Jack Weatherford mentions in Genghis Khan and the Making of the Modern World that the Mongols didn't invade India mainly because of climate. While the Mongols did invade hot climates, such as the middle east, the tropical climate of India did not suit the shaggy, cold weather steppe horses that the khanate used in the first round of conquests, and the climate in general made Genghis' men particularly sluggish. That compiled with the rugged Hindu kush that made supply trains a near impossibility, already mentioned in the previous comment, made a full scale invasion of India not only impossible but impractical, and so the Khan decided to bypass it for the easily accessible lands of central Asia.
I would disagree with the previous comment in that India, and northern India in particular, was a relatively wealthy land with a thriving civilization at the time, the Sultanate of Delhi. It would have been a prime target for Genghis Khan, if it had been convenient for him. His invasions seemed to pretty much follow the path of the silk road as well, hoping no doubt that he could control both end nodes, China and the Middle East, and India was a hefty detour from that objective.
hi, do check out this response from the FAQ by /u/MrBigHouse