Some evidence of Hindu/Buddhist thought is there in some of the passages in the gospels. For example John 1:1 also being found in many ancient pre-Christian Hindu texts as the starting point for chapters, clearly a possibility of Hindu influence. 

“In the beginning was the word, and the word was with Brahma, and the word was Brahma” 
(Krishna Yajurveda, Kathaka Samhita, 12.5, 27.1) 

A lot of what Jesus said about ethics parallels with Buddha's basic teaching. Jesus' experience of the three temptations in the wilderness is also paralleled with the Buddha. They are different temptations, but the existence of three temptations in the wilderness by Mara (Satan) is significant. Also you have some verses in the New Testament that hint at reincarnation theory, like when Jesus hinted at the idea that John the baptist actually was Elijah, 

"For all the prophets and the Law prophesied until John. And if you are willing to accept it, John himself is Elijah who was to come." (Matthew 11:13-15) 

Hindu conceptualization would also explain where Christianity conceived of the idea of incarnation in the form of an avatar outside of mere mythology. Some Christians would respond that Jesus' claim to uniqueness sets him apart from Hindu avatars, but those Hindu avatars also make similar claims of uniqueness. In the Gita we find Krishna making similar "I AM" claims. So this may be just God speaking in first person while incarnate in different individuals. 

"Of all creations I am the beginning and the end and also the middle, Arjuna. I am the spiritual science of the self, and I am the truth." (Gita 10:32)