Unfortunately the Naruto Manga has predominantly Buddhism and Shintoism influence, not Hinduism.
Naruto is a Samsaric Rebirth of Rikudou Sennin which is a Buddhist and not a Hindu concept, Buddhism unlike Hinduism does not believe in a permanent self (Anatta) therefore Naruto's Soul is Rikudou's Soul but their identity, memories are different from each other only sharing the Karmic imprints of the rebirthed soul.
Though one cannot deny the roots of modern buddhism are from hinduism, infact there are many more elements in Naruto that are in Hinduism. But this was a simple comparison =D.
As for the reincarnation, the reincarnation of the 3 mentioned in fact is similar to the one in Buddhism. Lord Ramma prayed and worshipped lord Vishnu, though he was his reincarnation. There are also different types of reincarnation in Hinduism alone. The one used in Buddhism is also derived from Hinduism.
Rebirth is a KIND of reincarnation. For example the religion of Sikhism, uses a different concept of reincarnation, but the roots are still the same.
Though in the thread, reincarnation isn't the focus =D
And then people deny the mythological and religious contrasts in the manga.. :devil:
lol. Its really weird. But the thing is some people like to predict what will happen in the manga and how things will be set up, by using mythology and religious contrasts.