I am a graduate student in partial differential equations. When I was reading the literature sometimes I came across concepts from geometry, such as curvature, Riemannian geometry, and so on.
I took differential geometry as an undergraduate but forgot a lot of it, and the textbooks at that time were biased towards differential geometry students, in other words I thought it was too specialized. So I want to review with another book.
So I would like to ask what is a relatively simple differential geometry textbook. My personal guess; It would suit me better if it was written by an expert in partial differential equations.
Note: My major is toward free boundary problems and fluid mechanics, not geometric analysis.