000			03375 a2200361 4500
003			NISER
005			20260109104603.0
008			260109b |||||||| |||| 00| 0 hin d
020			_a9783030460426 _qPaperback
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	4	_a514.747 _bGAL-D
100	1		_aGallier, Jean
245	1	0	_aDifferential geometry and lie groups : _ba computational perspective
260			_aCham, Switzerland : _bSpringer, _c2020.
300			_axv, 777 pages : _billustrations (1 b/w illustrations, 32 illustrations in colour) ; _c23 cm.
490			_aGeometry and computing ; _vvolume 12.
504			_aIncludes bibliographical references and index.
520			_aThis 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	_aGeometry
650		0	_aGeometry, Differential
650		0	_aLie groups
650		0	_aDifferential geometry for computing
650		0	_aDifferential geometry for machine learning
650		0	_aHomogeneous spaces
650		0	_aLorentz groups
650		0	_aRiemannian manifold
650		0	_aRiemannian manifold curvature
650		0	_aGrassmannian manifold
700	1		_aQuaintance, Jocelyn
856	4	1	_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-46040-2/1
856	4	1	_3Reviews _uhttps://www.goodreads.com/book/show/54696262-differential-geometry-and-lie-groups?ref=nav_sb_ss_1_13#CommunityReviews
942			_cBK _2udc
999			_c36730 _d36730