Gerard Walschap Metric Structures in Differential Geometry 9781441919137

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Автор: Gerard Walschap
Название: Metric Structures in Differential Geometry
ISBN: 9781441919137
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Геометрия

ISBN-10: 1441919139
Обложка/Формат: Paperback
Страницы: 229
Вес: 0.34 кг.
Дата издания: 29.11.2010
Серия: Graduate Texts in Mathematics
Язык: English
Размер: 234 x 156 x 13
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back- ground in calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are cov- ered, culminating in Stokes theorem together with some applications. The stu- dents first contact with the subject can be overwhelming because of the wealth of abstract definitions involved, so examples have been stressed throughout. One concept, for instance, that students often find confusing is the definition of tangent vectors. They are first told that these are derivations on certain equiv- alence classes of functions, but later that the tangent space of ffi.n is the same n as ffi. . We have tried to keep these spaces separate and to carefully explain how a vector space E is canonically isomorphic to its tangent space at a point. This subtle distinction becomes essential when later discussing the vertical bundle of a given vector bundle.

Metric Structures in Differential Geometry, Gerard Walschap