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Bücher Wissen & Bildung Englische Bücher Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Differential Geometry and Lie Groups
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Differential Geometry and Lie Groups
Jean Gallier, Jocelyn Quaintance (Broschiert, Englisch)
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Beschreibung
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 . Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
16.08.2021
Sprache
Englisch
EAN
9783030460426
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Geometry and Computing
Sonderedition
Nein
Autor
Jean Gallier, Jocelyn Quaintance
Seitenanzahl
777
Einbandart
Broschiert
Buch Untertitel
A Computational Perspective
Schlagwörter
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
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
PBG - Gruppen und Gruppentheorie
PBKS - Numerische Mathematik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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