A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition - Hardcover

Michael Spivak

Hardcover

ISBN 10: 0914098748 ISBN 13: 9780914098744

Publisher: Publish or Perish, 1999

Synopsis

A Comprehensive Introduction to Differential Geometry, Volume Five" by Michael Spivak is an essential resource for anyone interested in the intricate interplay of geometry, topology, and analysis. This advanced textbook delves into various topics in differential geometry, including partial differential equations (PDEs), isometric embeddings, rigidity, and the Gauss-Bonnet theorem. Key sections cover first-order PDEs, quasi-linear PDEs, characteristic curves, and free initial manifolds for higher-order equations. The book also explores non-imbeddability theorems, exteriorly orthogonal bilinear forms, and the Darboux equation. Readers will find detailed explanations, mathematical proofs, and numerous problems to solve, making it suitable for advanced students and researchers in mathematics. With its comprehensive coverage and in-depth analysis, this volume is a must-have for anyone looking to deepen their understanding of differential geometry.

About this title

About the Author

Michael David Spivak, born on May 25, 1940, is an American mathematician with a profound impact on the field of differential geometry. As an expositor of mathematics, he has skillfully bridged the gap between complex theory and accessible explanations. Spivak’s legacy extends beyond academia—he is also the visionary behind Publish-or-Perish Press. 📚 Author of the Five-Volume Masterpiece: Spivak’s magnum opus, “A Comprehensive Introduction to Differential Geometry,” stands as a testament to his mathematical prowess. This five-volume work is a treasure trove for those seeking a deep understanding of geometric concepts. 🔍 Why Choose Spivak? 🌟 Clarity and Precision: Spivak’s writing style demystifies intricate topics, making them approachable for learners at all levels. 🌟 Problem-Solving Focus: Dive into challenging problems guided by a master mathematician. 🌟 Mathematical Rigor: Immerse yourself in proofs, theorems, and applications—the hallmark of Spivak’s approach. 📖 About the Mathematician: Hailing from Queens, New York, Spivak earned his Ph.D. from Princeton University. His contributions have left an indelible mark on mathematics, and his passion for clarity continues to inspire generations of learners. 🛒 Explore Spivak’s Work: Whether you’re a student, educator, or lifelong learner, delve into the intricacies of calculus, geometry, and mathematical reasoning with Michael Spivak. 📚🔢

Excerpt. © Reprinted by permission. All rights reserved.

In "A Comprehensive Introduction to Differential Geometry, Volume Five," Michael Spivak provides an in-depth exploration of differential geometry. This advanced textbook covers a wide range of topics, including partial differential equations (PDEs), isometric embeddings, rigidity, and the Gauss-Bonnet theorem. The book delves into first-order PDEs, their classification, and methods for solving them, including the Cauchy problem and characteristic curves. It also addresses higher-order equations and systems of first-order PDEs. The text explores the existence and non-existence of isometric embeddings, including the Darboux equation and the Burstin-Janet-Cartan theorem. Rigidity is another key topic, with discussions on bendings, warpings, infinitesimal rigidity, and various theorems related to convex surfaces and higher codimension. The generalized Gauss-Bonnet theorem, characteristic classes, and the cohomology of homogeneous spaces are also covered in detail. The book includes detailed mathematical proofs, examples, and problems for further study, making it an essential resource for advanced students and researchers in the field of differential geometry.

Edition details

• Publisher: Publish or Perish
• Publication date: 1999
• ISBN 10: 0914098748
• ISBN 13: 9780914098744
• Binding: Hardcover
• Language: English
• Edition number: 3
• Number of pages: 467