Geometry and Computing

Differential Geometry and Lie Groups

A Second Course

Authors: Gallier, Jean, Quaintance, Jocelyn

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  • Explores the advanced mathematical theory behind modern geometry processing
  • Offers a uniquely accessible approach that is suitable for students and professionals alike
  • Augments core topics in advanced differential geometry with analytic and algebraic perspectives
  • Includes exercises throughout that are suitable for class use or independent study
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eBook 32,09 €
64,19 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-46047-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 39,51 €
77,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-46046-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing.  Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications.

Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions.

Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.

About the authors

Jean Gallier is Professor of Computer and Information Science at the University of Pennsylvania, Philadelphia. His research interests include geometry and its applications, geometric modeling, and differential geometry. He is also a member of the University of Pennsylvania’s Department of Mathematics, and its Center for Human Modelling and Simulation.

Jocelyn Quaintance is postdoctoral researcher at the University of Pennsylvania who has contributed to the fields of combinatorial identities and power product expansions. Her recent mathematical books investigate the interplay between mathematics and computer science. Covering areas as diverse as differential geometry, linear algebra, optimization theory, and Fourier analysis, her writing illuminates the mathematics behind topics relevant to engineering, computer vision, and robotics.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook 32,09 €
64,19 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-46047-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 39,51 €
77,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-46046-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Differential Geometry and Lie Groups
Book Subtitle
A Second Course
Authors
Series Title
Geometry and Computing
Series Volume
13
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-46047-1
DOI
10.1007/978-3-030-46047-1
Hardcover ISBN
978-3-030-46046-4
Series ISSN
1866-6795
Edition Number
1
Number of Pages
XIV, 620
Number of Illustrations
78 b/w illustrations, 32 illustrations in colour
Topics