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Titlebook: Lie Groups and Geometric Aspects of Isometric Actions; Marcos M. Alexandrino,Renato G. Bettiol Book 2015 Springer International Publishing

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发表于 2025-3-21 17:26:56 | 显示全部楼层 |阅读模式
书目名称Lie Groups and Geometric Aspects of Isometric Actions
编辑Marcos M. Alexandrino,Renato G. Bettiol
视频video
概述Includes an elementary introduction to Lie groups and Lie algebras.Uses a geometric approach that renders the text simultaneously complete and considerably short.Discusses recent topics on isometric a
图书封面Titlebook: Lie Groups and Geometric Aspects of Isometric Actions;  Marcos M. Alexandrino,Renato G. Bettiol Book 2015 Springer International Publishing
描述This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.
出版日期Book 2015
关键词Cheeger deformation; Frobenius theorem; Lie algebras; Lie groups; Riemannian geometry; Weyl group; cohomog
版次1
doihttps://doi.org/10.1007/978-3-319-16613-1
isbn_softcover978-3-319-38627-0
isbn_ebook978-3-319-16613-1
copyrightSpringer International Publishing Switzerland 2015
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发表于 2025-3-21 21:15:32 | 显示全部楼层
Lie Groups with Bi-invariant Metrics group admits a bi-invariant metric if and only if it is a product of a compact Lie group with a vector space (Theorem 2.45). Finally, we prove that if the Lie algebra of a compact Lie group . is simple, then the bi-invariant metric on . is unique up to rescaling (Proposition 2.48).
发表于 2025-3-22 03:28:01 | 显示全部楼层
nd considerably short.Discusses recent topics on isometric aThis book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas
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发表于 2025-3-22 12:40:22 | 显示全部楼层
Low Cohomogeneity Actions and Positive Curvature in the general case. Throughout this chapter, we emphasize connections between the geometry and topology of manifolds with low cohomogeneity stemming from curvature positivity conditions, such as positive (.) and nonnegative (.) sectional curvature.
发表于 2025-3-22 15:37:11 | 显示全部楼层
Book 2015any symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.
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发表于 2025-3-23 02:17:01 | 显示全部楼层
Marcos M. Alexandrino,Renato G. BettiolIncludes an elementary introduction to Lie groups and Lie algebras.Uses a geometric approach that renders the text simultaneously complete and considerably short.Discusses recent topics on isometric a
发表于 2025-3-23 07:22:48 | 显示全部楼层
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