000			nam a22 4500
999			_c32419 _d32419
008			230831b xxu||||| |||| 00| 0 eng d
020			_a9783030460426
082			_a516.36 _bGAL
100			_aGallier, Jean
245			_aDifferential geometry and Lie groups : a computational perspective
260			_bSpringer, _c2020 _aCham :
300			_axv, 777 p. ; _bill., (some color), _c24 cm
365			_b54.99 _cEUR _d94.90
490			_aGeometry and computing, _vv.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			_aMatrix Exponential
650			_aManifolds and Lie Groups
650			_aGeometry, Differential
650			_aTopological groups
700			_aQuaintance, Jocelyn
942			_2ddc _cBK