An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised – 2nd Edition Editor-in-Chiefs: William Boothby. Authors: William Boothby. MA Introduction to Differential Geometry and Topology William M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry. Here’s my answer to this question at length. In summary, if you are looking.

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Next, Boothby introduce us in the realm of Riemannian geometry: So I recommend that you read again the corresponding part of Boothby even though you experienced Spivak’s book. What is the meaning of a differenttial space?

Although basically and extension of advanced, or multivariable calculus, the leap from Euclidean space to manifolds can often be difficult. My web page subdivides DG books into the mathematics style and the physics style. The library has the version and one or more of the earlier editions, as well as the book.

Spivak’s book, Calculus on Manifolds, is a famous book about calculus on manifolds. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. It has become an In our class, we will stick to finite-dimensional manifolds, at least in the fall semester, and probably in the spring as well.

Differentiable manifolds and the differential and integral calculus of their associated structures, such as vectors, tensors, and differential forms are of great importance in many areas of mathematics and its applications. May 30 ’15 at 1: But I recommend that if you ever encounter differential manifold theory for the first time, then you solve a few exercises of the earlier part of the book.

But the book has overwhelmingly more good points. However, Lang writes in the generality needed for infinite-dimensional manifolds, requiring some comfort with infinite-dimensional Banach and Hilbert spaces on the part of the reader. Nor should one conclude anything from the order in which the books are listed—alphabetical by order within each group—or by comparing the lengths of different comments.


A beautiful book but presumes familiarity with manifolds. In addition to teaching at Washington University, he taught courses in subjects related to this text at the University of Cordoba Argentinathe University of Strasbourg Franceand the University of Perugia Italy.

Lectures on Differential Geometry. For that, I reread the differential geometry book by do Carmo and the book on Riemannian geometry by the same author, and I am really satisfied with the two books.

Amazon Renewed Refurbished products with a warranty. This is a well-written book for a first course in manifolds.

MA 562 Introduction to Differential Geometry and Topology

Showing of 9 reviews. Top Reviews Most recent Top Reviews. I would add one for the sake of physics. Line and surface integrals Divergence and curl of vector fields.

They have different objectives of course. My specialty was group theory. Many examples are given. Amazon Second Chance Pass it on, trade it in, give it a second life. To me, it seemed that the book is the easiest and the most reader-friendly, particularly for self-study. This is the only book available that is approachable by “beginners” in this subject. Amazon Advertising Find, attract, and engage customers. Maybe, an additional chapter is lacking, kind of a step further: Too much detail; volume 1 alone is pages.

I am falling in love with my life. Here are detailed points. Account Options Sign in. The sections are interesting but somewhat confusing since there was no definition of n-dimensional Euclidean space. Please someone tell me a book for Differential Geometry more advanced than Carmo’s book but readable esp. A valuable glimpse on symmetric spaces ends this chapter. I’m not done yet but went through more than half.


Tejas Kalelkar: Differential Geometry

BoothbyWilliam Munger Boothby. Within the first 40 pages, the book presents three equivalent definitions of tangent vectors. When I was a doctoral student, I studied geometry and topology. Academic Press; 2 edition August 19, Language: Immediately, the book deals with submanifolds and submersions, vector fields and their one parameter flows, the Lie algebra of smooth vector fields and the Frobenius theorem.

I also agree with another reviewer who gave 1 star that the often heavy notation doesn’t pay off here. I love the book, but it is not perfect. I don’t mean that they should follow every detail of proofs of theorems, but I mean that they should follow what the author is trying to say.

Lee’s book is if I remember correctly on the general theory of topological manifolds and probably covers some algebraic topology. There was a problem filtering reviews right now. Jacobi fields and cut loci, tubullar neighbourhoods and their volumes, Rauch comparison theorem For a first course in manifolds, this may be daunting and may hinder the development of intuition. Amitesh Datta Hi, the reference for graduate level that I need to cover it as a first direction to go is “W M Boothby – An Introduction to Differentiable Manifolds and and Riemannian Geometry” which is not readable despite its appearance!

They are important, so readers should carefully read the part. The process of reading the book in a continuous fashion, while certainly rewarding, has also led to significant disappointment.