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

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定點

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).

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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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偉大

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.

BADGE

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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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

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