This book is an introduction to the fundamentals of differential geometry that covers manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It stresses naturality and functoriality and is coordinate-free as possible. The Laplace-Beltrami operator is treated only summarily, there is no spectral theory, and the structure theory of Lie algebras is not discussed. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)
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Book by Peter W Michor
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Condizione: New. Treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. This book covers a wide range of topics of modern coordinate-free differential geometry. Series: Graduate Studies in Mathematics. Num Pages: 493 pages, Illustrations. BIC Classification: PBMP. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 259 x 186 x 30. Weight in Grams: 1066. . 2008. Hardcover. . . . . Codice articolo V9780821820032
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Da: Kennys Bookstore, Olney, MD, U.S.A.
Condizione: New. Treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. This book covers a wide range of topics of modern coordinate-free differential geometry. Series: Graduate Studies in Mathematics. Num Pages: 493 pages, Illustrations. BIC Classification: PBMP. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 259 x 186 x 30. Weight in Grams: 1066. . 2008. Hardcover. . . . . Books ship from the US and Ireland. Codice articolo V9780821820032
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Buch. Condizione: Neu. Neuware - This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. The layout of the material stresses naturality and functoriality from the beginning and is as coordinate-free as possible. Coordinate formulas are always derived as extra information. Some attractive unusual aspects of this book are as follows: Initial submanifolds and the Frobenius theorem for distributions of nonconstant rank (the Stefan-Sussman theory) are discussed. Lie groups and their actions are treated early on, including the slice theorem and invariant theory. De Rham cohomology includes that of compact Lie groups, leading to the study of (nonabelian) extensions of Lie algebras and Lie groups. The Frolicher-Nijenhuis bracket for tangent bundle valued differential forms is used to express any kind of curvature and second Bianchi identity, even for fiber bundles (without structure groups).Riemann geometry starts with a careful treatment of connections to geodesic structures to sprays to connectors and back to connections, going via the second and third tangent bundles. The Jacobi flow on the second tangent bundle is a new aspect coming from this point of view. Symplectic and Poisson geometry emphasizes group actions, momentum mappings, and reductions.This book gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra. Codice articolo 9780821820032
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