Geometry VI (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
504
Utgivningsdatum
2010-12-09
Upplaga
Softcover reprint of the original 1st ed. 2001
Förlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Illustrationer
XVIII, 504 p.
Volymtitel
v. 6
Dimensioner
234 x 156 x 27 mm
Vikt
726 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9783642074349

Geometry VI

Riemannian Geometry

av M M Postnikov
Häftad,  Engelska, 2010-12-09
1340
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The original Russian edition of this book is the fifth in my series "Lectures on Geometry. " Therefore, to make the presentation relatively independent and self-contained in the English translation, I have added supplementary chapters in a special addendum (Chaps. 3Q-36), in which the necessary facts from manifold theory and vector bundle theory are briefly summarized without proofs as a rule. In the original edition, the book is divided not into chapters but into lec tures. This is explained by its origin as classroom lectures that I gave. The principal distinction between chapters and lectures is that the material of each chapter should be complete to a certain extent and the length of chapters can differ, while, in contrast, all lectures should be approximately the same in length and the topic of any lecture can change suddenly in the middle. For the series "Encyclopedia of Mathematical Sciences," the origin of a book has no significance, and the name "chapter" is more usual. Therefore, the name of subdivisions was changed in the translation, although no structural surgery was performed. I have also added a brief bibliography, which was absent in the original edition. The first ten chapters are devoted to the geometry of affine connection spaces. In the first chapter, I present the main properties of geodesics in these spaces. Chapter 2 is devoted to the formalism of covariant derivatives, torsion tensor, and curvature tensor. The major part of Chap.
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Fler böcker av M M Postnikov

  • Foundations of Galois Theory

    Foundations of Galois Theory

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    Compact, self-contained text by a noted theorist presents essentials of modern differential geometry and basic tools for study of Morse theory. Advanced treatment emphasizes Morse theory's analytical rather than topological aspects. 1967 edition.

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Recensioner i media

From the reviews of the first edition: "... The book is .. comprehensive and original enough to be of interest to any professional geometer, but I particularly recommend it to the advanced student, who will find a host of instructive examples, exercises and vistas that few comparable texts offer... " H.Geiges, Nieuw Archief voor Wiskunde 2002, Vol. 5/3, Issue 4 "... I found the presentation insightful and stimulating. A useful paedagogical device of the text is to make much use of both the index and coordinate-free notations, encouraging flexibility (and pragmatism) in the reader. ... the book should be of use to a wide variaty of readers: the relative beginner, with perhaps an introductory course in differential geometry, will find his horizons greatly expanded in the material for which this prepares him; while the more experienced reader will surely find the more specialised sections informative." Robert J. Low, Mathematical Reviews, Issue 2002g "... Insgesamt liegt ein sehr empfehlenswertes Lehrbuch einerseits zur Riemannschen Geometrie und andererseits zur Theorie differenzierbarer Mannigfaltigkeiten vor, wegen der strukturierten Breite der Darstellung sehr gut geeignet sowohl zum Selbststudium fr Studierende mathematischer Disziplinen als auch fr Dozenten als Grundlage einschlgiger Lehrveranstaltungen." P. Paukowitsch, Wien (IMN - Internationale Mathematische Nachrichten 190, S. 64-65, 2002) "M.M. Postnikov has written a well-structured and readable book with a satisfying sense of completeness to it. The reviewer believes this book deserves a place next to the already existing literature on Riemannian geometry, principally as a basis for teaching a course on abstract Riemannian geometry (after an introduction to differentiable manifolds) but also as a reference work." (Eric Boeckx, Zentralblatt MATH, Vol. 993 (18), 2002)

Innehållsförteckning

1. Affine Connections.- 2. Covariant Differentiation. Curvature.- 3. Affine Mappings. Submanifolds.- 4. Structural Equations. Local Symmetries.- 5. Symmetric Spaces.- 6. Connections on Lie Groups.- 7. Lie Functor.- 8. Affine Fields and Related Topics.- 9. Cartan Theorem.- 10. Palais and Kobayashi Theorems.- 11. Lagrangians in Riemannian Spaces.- 12. Metric Properties of Geodesics.- 13. Harmonic Functionals and Related Topics.- 14. Minimal Surfaces.- 15. Curvature in Riemannian Space.- 16. Gaussian Curvature.- 17. Some Special Tensors.- 18. Surfaces with Conformal Structure.- 19. Mappings and Submanifolds I.- 20. Submanifolds II.- 21. Fundamental Forms of a Hypersurface.- 22. Spaces of Constant Curvature.- 23. Space Forms.- 24. Four-Dimensional Manifolds.- 25. Metrics on a Lie Group I.- 26. Metrics on a Lie Group II.- 27. Jacobi Theory.- 28. Some Additional Theorems I.- 29. Some Additional Theorems II.- Addendum.- 30. Smooth Manifolds.- 31. Tangent Vectors.- 32. Submanifolds of a Smooth Manifold.- 33. Vector and Tensor Fields. Differential Forms.- 34. Vector Bundles.- 35. Connections on Vector Bundles.- 36. Curvature Tensor.- Bianchi Identity.- Suggested Reading.

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