A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition (pre-owned)

A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition by Michael Spivak

Discover the advanced world of differential geometry with "A Comprehensive Introduction to Differential Geometry, Volume Two, Third Edition" by Michael Spivak. Published by Publish or Perish, Inc. in Houston, Texas, this authoritative guide delves into intricate details of differential geometry, providing a thorough understanding through historical context, theoretical foundations, and advanced mathematical formulations.

This volume follows a semi-historical path, focusing on classical differential geometry in Chapters 3 and 4. Although it lacks problem sets, it compensates with a comprehensive bibliography in the final volume. Key topics include:

• Curves in the plane and in space
• The curvature of surfaces in space
• The curvature of higher-dimensional manifolds
• The absolute differential calculus (Ricci calculus)
• The r operator
• The repère mobile (moving frame)
• Connections in principal bundles

An excerpt from the book specifically discusses Gauss' investigations of curved surfaces, providing detailed explanations and proofs of various geometric properties and theorems related to the curvature of surfaces. This section combines historical context, mathematical rigor, and detailed proofs to explore the fundamental aspects of differential geometry, focusing on Gauss' contributions and Riemann's advancements.

Overall, this book is a valuable resource for anyone looking to deepen their understanding of differential geometry. It offers a comprehensive and authoritative guide to the subject, making it an essential addition to your collection.