|
|
libcats.org
Metric structures in differential geometryGerard WalschapThis text is an introduction to the theory of differentiable manifolds and fiber bundles. The only requisites are a solid background in calculus and linear algebra, together with some basic point-set topology. The first chapter provides a comprehensive overview of differentiable manifolds. The following two chapters are devoted to fiber bundles and homotopy theory of fibrations. Vector bundles have been emphasized, although principal bundles are also discussed in detail. The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres. Chapter 5, with its focus on the tangent bundle, also serves as a basic introduction to Riemannian geometry in the large. This book can be used for a one-semester course on manifolds or bundles, or a two-semester course in differential geometry. Gerard Walschap is Professor of Mathematics at the University of Oklahoma where he developed this book for a series of graduate courses he has taught over the past few years.
Популярные книги за неделю:
Проектирование и строительство. Дом, квартира, садАвтор: Петер Нойферт, Автор: Людвиг Нефф
Размер книги: 20.83 Mb
Система упражнений по развитию способностей человека (Практическое пособие)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 818 Kb
Сотворение мира (3-х томник)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 817 Kb
Радиолюбительские схемы на ИС типа 555Автор: Трейстер Р.Категория: Электротехника и связь
Размер книги: 13.64 Mb
Момент истины (В августе сорок четвертого...)Автор: Богомолов Владимир ОсиповичКатегория: О войне
Размер книги: 1.83 Mb
Только что пользователи скачали эти книги:
Vibro-impact dynamics: Modeling, mapping and applicationsАвтор: Raouf A. IbrahimКатегория: E_Engineering
Размер книги: 4.69 Mb
The Fortran 2003 Handbook: The Complete Syntax, Features and ProceduresАвтор: Jeanne C. Adams, Автор: Walter S. Brainerd, Автор: Richard A. Hendrickson, Автор: Richard E. Maine, Автор: Jeanne T. Martin, Автор: Brian T. Smith
Размер книги: 4.10 Mb
Sport and Tourism: Globalization, mobility and IdentityАвтор: James Higham, Автор: Tom Hinch
Размер книги: 2.00 Mb
Polarities of Experiences: Relatedness and Self-definition in Personality Development, Psychopathology and the Therapeutic ProcessАвтор: Sidney J. Blatt
Размер книги: 25.63 Mb
Preserving Food Without Freezing Or Canning: Traditional Techniques Using Salt, Oil, Sugar, Alcohol, Vinegar, Drying, Cold Storage, and Lactic FermentationАвтор: Deborah Madison
Размер книги: 11.57 Mb
Tratado de la reforma del entendimientoАвтор: Spinoza BaruchКатегория: fiction
Размер книги: 242 Kb
|
|
|