Differential Geometry and Lie Groups: A Computational Perspective

Book Details

• Publisher: Springer

• Author: Gallier, Jean

• Language: English

• Edition: 2020 ed.

• ISBN: 9783030460426

• Pages: 777

• Cover: Paperback

• Dimensions: 9.3 x 6.2 x 1.5 inches

About The Book

Differential Geometry and Lie Groups: A Computational Perspective by Jean Gallier, published by Springer, provides a modern and accessible introduction to differential geometry tailored for students and professionals working in geometry processing, computer vision, robotics, and machine learning. With 777 pages of comprehensive content, this 2020 edition is perfectly suited for classroom instruction or independent study, requiring only a background in calculus and linear algebra.

The text begins with an introduction to Lie groups and group actions, using the matrix exponential as a launching point. It then builds up manifold theory, including tangent and cotangent spaces, vector fields, and point-set topology. A dedicated chapter on manifold construction from gluing data bridges theoretical geometry with practical applications like 3D mesh reconstruction.

The second part of the book dives into Riemannian geometry, covering key topics such as Riemannian metrics, geodesics, curvature, submersions, and the Log-Euclidean framework. The final chapter introduces naturally reductive homogeneous manifolds and symmetric spaces, preparing readers to apply these concepts in manifold optimization techniques.

Packed with exercises and optional deeper explorations, this book offers a balanced approach to both computation and theory. It is an ideal gateway for those seeking a strong mathematical foundation behind many advanced computational applications. Readers planning to pursue deeper topics will benefit from the companion volume Differential Geometry and Lie Groups: A Second Course.