Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition

Book Details

• Publisher: Dover

• Author: Manfredo P. Do Carmo

• Language: English

• Edition: 2

• ISBN: 9780486806990

• Pages: 512

• Cover: Paperback

• Dimensions: 9.0 x 6.0 x 1.1 inches

About The Book

Differential Geometry of Curves and Surfaces by Manfredo P. Do Carmo, published by Dover, is one of the most respected and widely used textbooks in the field of differential geometry. This second edition provides a comprehensive and accessible introduction to both the local and global aspects of the subject, making it ideal for advanced undergraduates and graduate students in mathematics.

Departing from traditional approaches, Do Carmo emphasizes fundamental geometric insights and the practical application of elementary linear algebra, rather than relying on complex machinery or abstract formalism. The book begins with an exploration of curves, then progresses to regular surfaces, the geometry of the Gauss map, intrinsic geometry, and culminates in global differential geometry. The clear exposition is supported by numerous examples, exercises, and helpful hints, with answers included for selected problems to facilitate independent study.

Prerequisites include an undergraduate-level understanding of linear algebra and multivariable calculus. This revised and updated edition reflects the author's dedication to clarity, accuracy, and pedagogical effectiveness. A cornerstone in the study of geometry, this 512-page paperback remains an essential reference for anyone pursuing deeper insights into the beauty and structure of curves and surfaces.