![]() ![]() I love Guillemin and Pollack, but it is just a rewrite for undergraduates of Milnor's "Topology from a Differentiable Viewpoint". 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. Around 200 additional exercises, and a full solutions manual for instructors, available via 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. Around 200 additional exercises, and a full solutions manual for instructors, available via Description Coverage of topics such as: parallel transport and its applications map colouring holonomy and Gaussian curvature. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. New features of this revised and expanded second edition include: Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.Įlementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. ![]() Differential geometry is concerned with the precise mathematical formulation of some of these questions. Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. ![]()
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