Buch, Englisch, Band 13, 620 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1225 g
Reihe: Geometry and Computing
A Second Course
Buch, Englisch, Band 13, 620 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1225 g
Reihe: Geometry and Computing
ISBN: 978-3-030-46046-4
Verlag: Springer International Publishing
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.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
1. Tensor Algebras.- 2. Exterior Tensor Powers and Exterior Algebras.- 3. Differential Forms.- 4. Distributions and the Frobenius Theorem.- 5. Integration on Manifolds.- 6. Spherical Harmonics and Linear Representations.- 7. Operators on Riemannian Manifolds.- 8. Bundles, Metrics on Bundles, Homogeneous Spaces.- 9. Connections and Curvature in Vector Bundles.- 10. Clifford Algebras, Clifford Groups, Pin and Spin.