Spivack is for me way too verbose and makes easy things look too complicated and difficult. Of course, this is a natural thing to do, while you're trying to work out your own proof anyway. So you'll go nuts, unless you have your own notation and you translate whatever you're reading into your own notation. Why? Because it appears that each differential geometer and therefore each differential geometry book uses its own notation different from everybody else's. Second, follow the advice of another former Harvard professor and develop your own notation. My interpretation of this is to look first at only the statements of the definitions and theorems and try to work out the proofs yourself. He would point to a book or paper and say, "You should know everything in here but don't read it!". One of them, Degeneration of Riemannian metrics under Ricci curvature bounds, is available on Amazon.įirst, follow the advice that a former Harvard math professor used to give his students. They lay the groundwork for his recent work on Ricci curvature. He is relying on notes he has written, which I can recommend, at least for a nice overview of the subject. So far, I like Petersen's book best.Īlso, as it happens, Cheeger is teaching a topics course on Ricci curvature. In particular, I wanted to do global Riemannian geometric theorems, up to at least the Cheeger-Gromoll splitting theorem. I also wanted to focus on differential geometry and not differential topology. I am teaching a graduate differential geometry course focusing on Riemannian geometry and have been looking more carefully at several textbooks, including those by Lee, Tu, Petersen, Gallot et al, Cheeger-Ebin.
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