Differential Geometry

Araújo, Paulo Ventura

  • 出版商: Springer
  • 出版日期: 2024-07-09
  • 售價: $2,240
  • 貴賓價: 9.5$2,128
  • 語言: 英文
  • 頁數: 185
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031623835
  • ISBN-13: 9783031623837
  • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This textbook provides a concise introduction to the differential geometry of curves and surfaces in three-dimensional space, tailored for undergraduate students with a solid foundation in mathematical analysis and linear algebra.

The book emphasizes the geometric content of the subject, aiming to quickly cover fundamental topics such as the isoperimetric inequality and the Gauss-Bonnet theorem. This approach allows the author to extend beyond the typical content of introductory books and include additional important geometric results, such as curves and surfaces of constant width, the classification of complete surfaces of non-negative constant curvature, and Hadamard's theorem on surfaces of non-positive curvature. This range of topics offers greater variety for an introductory course.

商品描述(中文翻譯)

本教科書提供了三維空間中曲線和曲面的微分幾何的簡明介紹,專為具備堅實數學分析和線性代數基礎的本科生量身打造。

本書強調該主題的幾何內容,旨在迅速涵蓋基本主題,如等周不等式和高斯-博內定理。這種方法使作者能夠超越入門書籍的典型內容,並包含其他重要的幾何結果,例如常寬曲線和曲面、非負常曲率的完整曲面的分類,以及哈達馬爾定理在非正曲率曲面上的應用。這一系列主題為入門課程提供了更大的多樣性。

作者簡介

Paulo Ventura Araújo graduated with a degree in Mathematics from the University of Porto and obtained his doctorate from the University of Warwick. Currently, he is a professor at the Faculty of Sciences in Porto.

作者簡介(中文翻譯)

保羅·文圖拉·阿拉烏喬(Paulo Ventura Araújo)畢業於波爾圖大學,獲得數學學位,並在華威大學取得博士學位。目前,他是波爾圖科學院的教授。