Shoshichi Kobayashi Differential Geometry of Curves and Surfaces 9789811517389

Варианты приобретения

Цена: 4890.00р.
Кол-во:
Наличие: Поставка под заказ. Есть в наличии на складе поставщика.
Склад Америка: Есть
При оформлении заказа до: 2025-07-28
Ориентировочная дата поставки: Август-начало Сентября
При условии наличия книги у поставщика.

Добавить в корзину

в Мои желания

Автор: Shoshichi Kobayashi
Название: Differential Geometry of Curves and Surfaces
ISBN: 9789811517389
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Дифференциальная и риманова геометрия

Топология

ISBN-10: 981151738X
Обложка/Формат: Soft cover
Страницы: 192
Вес: 0.32 кг.
Дата издания: 2019
Серия: Springer Undergraduate Mathematics Series
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 110 illustrations, black and white; x, 190 p. 110 illus.
Размер: 234 x 156 x 11
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
Рейтинг:
Поставляется из: Германии
Описание:

This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces. Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature K and the mean curvature H —are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain. Then the Gauss–Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number ?(S). Here again, many illustrations are provided to facilitate the reader’s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.

Дополнительное описание: Plane Curves and Space Curves.- Local Theory of Surfaces in the Space.- Geometry of Surfaces.- The Gauss-Bonnet Theorem.- Minimal Surfaces.

Differential Geometry of Curves and Surfaces, Shoshichi Kobayashi