Differential Geometry and Lie Groups: A Second Course

This textbook covers advanced topics in differential geometry, with an emphasis on their relevance to modern geometry processing. It begins with an in-depth study of tensors and differential forms and then explores topics such as distributions, integration on manifolds, Lie groups, spherical harmonics, and operators on Riemannian manifolds. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion. The text is suitable for classroom use or independent study and assumes a first course in differential geometry.

Format: Paperback / softback
Length: 620 pages
Publication date: 19 August 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook delves into advanced topics in differential geometry, carefully selected for their significant relevance to modern geometry processing. By incorporating both analytic and algebraic perspectives, the authors aim to provide a comprehensive understanding of these mathematical concepts. Whether readers are pursuing theoretical or applied inquiries, this accessible exploration of the underlying mathematical principles behind numerous modern applications will be invaluable.

The text begins with an in-depth exploration of tensors and differential forms, laying the foundation for subsequent chapters. These chapters cover a range of topics, including distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An analytic theme runs throughout the early chapters, unifying these diverse subjects.

The next section delves into bundles, beginning with their definitions and progressing to connections and curvature in vector bundles. The culmination of this exploration is a brief glimpse into Pontrjagin and Chern classes, which offer a deeper understanding of the mathematical structures involved.

The final chapter brings the book to an algebraic conclusion, focusing on Clifford algebras and Clifford groups. This chapter serves as a generalized viewpoint of the quaternions, providing a comprehensive understanding of the mathematical theory underpinning these important concepts.

Differential Geometry and Lie Groups: A Second Course is designed for classroom use or independent study. It assumes a foundational knowledge of differential geometry, and its companion volume, Differential Geometry and Lie Groups: A Computational Perspective, offers an ideal preparation for those seeking to delve deeper into this field.

By presenting these advanced topics in a clear and accessible manner, this textbook serves as a valuable resource for students, researchers, and professionals alike. Its comprehensive coverage and interdisciplinary approach make it an essential tool for anyone interested in advancing their understanding of differential geometry and its applications in modern geometry processing.

Weight: 961g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030460495
Edition number: 1st ed. 2020