東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ subject:"Differential Geometry." ]

切換: 標籤 | MARC模式 | ISBD

Differential geometry and Lie groups...

Gallier, Jean.

FindBook

Google Book

Amazon

博客來

Differential geometry and Lie groups = a computational perspective /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Differential geometry and Lie groups/ by Jean Gallier, Jocelyn Quaintance.
其他題名:	a computational perspective /
作者:	Gallier, Jean.
其他作者:	Quaintance, Jocelyn.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xv, 777 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Geometry, Differential. -
電子資源:	https://doi.org/10.1007/978-3-030-46040-2
ISBN:	9783030460402

Differential geometry and Lie groups = a computational perspective /
Gallier, Jean.

Differential geometry and Lie groupsa computational perspective /[electronic resource] :by Jean Gallier, Jocelyn Quaintance. - Cham :Springer International Publishing :2020. - xv, 777 p. :ill., digital ;24 cm. - Geometry and computing,v.121866-6795 ;. - Geometry and computing ;v.12..

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, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors' companion volume Differential Geometry and Lie Groups: A Second Course.

ISBN: 9783030460402

Standard No.: 10.1007/978-3-030-46040-2doiSubjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641 / .G355 2020

Dewey Class. No.: 516.36

Differential geometry and Lie groups = a computational perspective /
LDR:04053nmm a2200337 a 4500 001 2256037
003 DE-He213
005 20201228114116.0
006 m d
007 cr nn 008maaau
008 220420s2020 sz s 0 eng d
020 $a 9783030460402 $q (electronic bk.)
020 $a 9783030460396 $q (paper)
024 7 $a 10.1007/978-3-030-46040-2 $2 doi
035 $a 978-3-030-46040-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA641 $b .G355 2020
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 516.36 $2 23
090 $a QA641 $b .G168 2020
100 1 $a Gallier, Jean. $3 3526017
245 1 0 $a Differential geometry and Lie groups $h [electronic resource] : $b a computational perspective / $c by Jean Gallier, Jocelyn Quaintance.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xv, 777 p. : $b ill., digital ; $c 24 cm.
490 1 $a Geometry and computing, $x 1866-6795 ; $v v.12
505 0 $a 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.
520 $a 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, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors' companion volume Differential Geometry and Lie Groups: A Second Course.
650 0 $a Geometry, Differential. $3 523835
650 0 $a Lie groups. $3 526114
650 1 4 $a Differential Geometry. $3 891003
650 2 4 $a Topological Groups, Lie Groups. $3 891005
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
700 1 $a Quaintance, Jocelyn. $3 3470124
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Geometry and computing ; $v v.12. $3 3526018
856 4 0 $u https://doi.org/10.1007/978-3-030-46040-2
950 $a Mathematics and Statistics (SpringerNature-11649)