Differential Geometry and Lie Groups : A Computational Perspective. 1st ed. 2020
- 種類:
- 電子ブック
- 責任表示:
- by Jean Gallier, Jocelyn Quaintance
- 出版情報:
- Cham : Springer International Publishing : Imprint: Springer, 2020
- 著者名:
- シリーズ名:
- Geometry and Computing ; 12
- ISBN:
- 9783030460402 [3030460401]
- 注記:
- 1. The Matrix Exponential; Some Matrix Lie Groups -- 2. Adjoint Representations and the Derivative of exp -- 3. Introduction to Manifolds and Lie Groups -- 4. Groups and Group Actions -- 5. The Lorentz Groups ⊛ -- 6. The Structure of O(p,q) and SO(p, q) -- 7. Manifolds, Tangent Spaces, Cotangent Spaces -- 8. Construction of Manifolds From Gluing Data ⊛ -- 9. Vector Fields, Integral Curves, Flows -- 10. Partitions of Unity, Covering Maps ⊛ -- 11. Basic Analysis: Review of Series and Derivatives -- 12. A Review of Point Set Topology.-13. Riemannian Metrics, Riemannian Manifolds -- 14. Connections on Manifolds -- 15. Geodesics on Riemannian Manifolds -- 16. Curvature in Riemannian Manifolds -- 17. Isometries, Submersions, Killing Vector Fields -- 18. Lie Groups, Lie Algebra, Exponential Map -- 19. The Derivative of exp and Dynkin's Formula ⊛ -- 20. Metrics, Connections, and Curvature of Lie Groups -- 21. The Log-Euclidean Framework -- 22. Manifolds Arising from Group Actions.
This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics - ローカル注記:
- 岐阜大学構成員専用E-BOOKS (Gifu University members only)
類似資料:
Springer International Publishing : Imprint: Springer |
Springer International Publishing : Imprint: Springer |
Springer Netherlands : Imprint: Springer |
Springer Berlin Heidelberg : Imprint: Springer |
3
電子ブック
Lie Groups, Geometry, and Representation Theory : A Tribute to the Life and Work of Bertram Kostant
Springer International Publishing : Imprint: Birkhäuser |
Springer Science+Business Media, LLC |
Springer Berlin Heidelberg : Imprint: Springer |
10
電子ブック
Discrete Mechanics, Geometric Integration and Lie–Butcher Series : DMGILBS, Madrid, May 2015
Springer International Publishing : Imprint: Springer |
Springer Berlin Heidelberg : Imprint: Springer |
Springer Berlin Heidelberg : Imprint: Springer |
Springer International Publishing : Imprint: Springer |
Springer Berlin Heidelberg : Imprint: Springer |