Differential Geometry of Curves and Surfaces

by Manfredo P. Do Carmo

This volume covers local as well as global differential geometry of curves and surfaces.

Genres: Mathematics, Textbooks, Geometry, Science, Physics, Technical, Nonfiction

503 pages, Hardcover

First published February 11, 1976

About the author

Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil.

Reviews

[Mark Moon]

This book features a rather nice collection of examples of interesting curves and surfaces. The treatment is rather old-fashioned; manifolds are always embedded in a euclidean space until the very end. It would be an ok book if not for the high frequency of confusing typos.

[Robert]

Took an undergraduate differential geometry course (M435) out of this book at Indiana University. Very clear introduction, but be warned: many of the problems and examples contain dangerously subtle typos. Many times I would be stuck on a problem for hours only to realize that there was an error in the description of the problem.

[Kai]

quality textbook would recommend to a friend

[Tpinetz]

I did a course on differential geometry and read this book as a guide and it worked well for that. A lot of additional exercises are included and it's not hard to follow along. However, I think its a shame that manifold theory is not included at all.

[C. Hinsley]

Dr. Theodore Shifrin's introductory differential geometry text is better (more concise, prettier notation, less errata), but this book is good as a standalone or as supplement, covering some things that Shifrin's text does not. This book sacrifices some clarity and gains a bit of comprehensiveness.

[Sabrina]

this is a decent differential geometry book.... I wish it had more detail than it did... I've found that sometimes certain chapters felt overly lack luster... this book had potential but it needed so much more than it had..

[Fan Wang]

Very clear and detailed

[estrabismo]

I went through the 4/5 chapters with auditing a class. The appendices made the book pretty self-contained and much appreciated. I liked the presentation of definitions, propositions, and proofs. I think the perspective was more or less friendly to people who have taken math classes geared towards science students (vector calc + linear algebra) with mild theory, although I have not read other textbooks on the same subject. As companion texts, I used Mary Boas's 'Mathematical Methods in the Physical Sciences,' for technical refreshing and David Hilbert's 'Geometry & the Imagination.' The latter is leisurely and gives intuition and visualization which is helpful, although topics are introduced in very different order than do Carmo. I also must give much credit to the professor who taught the course. She was fantastic.

[Gabriel Ferreira]

Although I tried other textbooks and could not find one better than this, I wish this book (and the other ones I tried) had more explanations, including explanations on the intuition and solved exercises. Since I can't point a better book I am giving it 4 stars, instead of 3.
PS: maybe Tristan Needham book "Visual Differential Geometry and Forms" (I think it will be released in 2021) could complement this one nicely.

[DJ]

good advanced text for after Pressley

[Mark Hoyle]

Excellent treatise on curves and surfaces with very clear exposition of the motivation behind many concepts in Riemannian Geometry.