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Differential geometry and Lie groups: a second course

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied ques...

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Detalles Bibliográficos
Autores principales: Gallier, Jean, Quaintance, Jocelyn
Lenguaje:eng
Publicado: Springer 2020
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-46047-1
http://cds.cern.ch/record/2729467
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author Gallier, Jean
Quaintance, Jocelyn
author_facet Gallier, Jean
Quaintance, Jocelyn
author_sort Gallier, Jean
collection CERN
description This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
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spelling cern-27294672021-04-21T18:05:10Zdoi:10.1007/978-3-030-46047-1http://cds.cern.ch/record/2729467engGallier, JeanQuaintance, JocelynDifferential geometry and Lie groups: a second courseMathematical Physics and MathematicsThis textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.Springeroai:cds.cern.ch:27294672020
spellingShingle Mathematical Physics and Mathematics
Gallier, Jean
Quaintance, Jocelyn
Differential geometry and Lie groups: a second course
title Differential geometry and Lie groups: a second course
title_full Differential geometry and Lie groups: a second course
title_fullStr Differential geometry and Lie groups: a second course
title_full_unstemmed Differential geometry and Lie groups: a second course
title_short Differential geometry and Lie groups: a second course
title_sort differential geometry and lie groups: a second course
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-46047-1
http://cds.cern.ch/record/2729467
work_keys_str_mv AT gallierjean differentialgeometryandliegroupsasecondcourse
AT quaintancejocelyn differentialgeometryandliegroupsasecondcourse