One of my friend who is an undergraduate student, has known something about algebraic geometry (equivalent to chapter 1 and a little bit chapter 2 in GTM 52 by Hartshorne). He is now has to study a differential geometry course. Since there are a lot of Differential geometry text books with different intention, he asked me what he should learn in differential geometry so that it helps him to improve his knowledge in algebraic geometry
I can not answer this question so I decided to post it here. Please help him.