M. M. Postnikov: Geometry VI | Taschenbuch

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Cover: 9783642074349 | Geometry VI | Riemannian Geometry | M. M. Postnikov | Taschenbuch

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

A well-written introduction to the subject

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2010
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	524
Reihe:	Encyclopaedia of Mathematical Sciences
Inhalt:	xviii 504 S. 7 s/w Illustr.
ISBN-13:	9783642074349
ISBN-10:	3642074340
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Postnikov, M. M.
Auflage:	Softcover reprint of the original 1st ed. 2001
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Encyclopaedia of Mathematical Sciences
Maße:	235 x 155 x 29 mm
Von/Mit:	M. M. Postnikov
Erscheinungsdatum:	09.12.2010
Gewicht:	0,785 kg

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