Differential Geometry and Lie Groups
portes grátis
Differential Geometry and Lie Groups
A Computational Perspective
Quaintance, Jocelyn; Gallier, Jean
Springer Nature Switzerland AG
08/2021
777
Mole
Inglês
9783030460426
15 a 20 dias
1400
Descrição não disponível.
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.
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Differential geometry for computing;differential geometry for geometry processing;differential geometry textbook;differential geometry for computer vision;differential geometry for robotics;differential geometry for machine learning;homogeneous spaces;matrix lie groups;matrix exponential;adjoint representation;linear lie groups;grassmannian manifold;stiefel manifold;lie algebras for computing;lie brackets;Lorentz groups;Riemannian manifold;Riemannian manifold curvature;Connections on real manifolds;Theory of manifold optimization techniques
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Differential geometry for computing;differential geometry for geometry processing;differential geometry textbook;differential geometry for computer vision;differential geometry for robotics;differential geometry for machine learning;homogeneous spaces;matrix lie groups;matrix exponential;adjoint representation;linear lie groups;grassmannian manifold;stiefel manifold;lie algebras for computing;lie brackets;Lorentz groups;Riemannian manifold;Riemannian manifold curvature;Connections on real manifolds;Theory of manifold optimization techniques
