Differential Geometry
暫譯: 微分幾何
Prasolov, Victor V., Sipacheva, Olga
- 出版商: Springer
- 出版日期: 2023-02-11
- 售價: $2,360
- 貴賓價: 9.5 折 $2,242
- 語言: 英文
- 頁數: 271
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3030922510
- ISBN-13: 9783030922511
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商品描述
The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups.
商品描述(中文翻譯)
本書結合了經典與當代的微分幾何方法。在介紹流形的黎曼幾何之前，詳細討論了曲線和曲面的性質。
有關平面曲線的微分幾何章節考慮了曲線的局部和全局性質、演變曲線和反演曲線，以及仿射和射影微分幾何。書中討論了多種方法來計算曲面的高斯曲率。曲率張量、共軛點和拉普拉斯-貝爾特拉米算子首先在二維曲面上詳細考慮，這有助於在多維情況下進行研究。另有一章專門探討李群的微分幾何。
作者簡介
Victor Prasolov, born 1956, is a permanent teacher of mathematics at the Independent University of Moscow. He published two books with Springer, Polynomials and Algebraic Curves. Towards Moduli Spaces (jointly with M. E. Kazaryan and S. K. Lando) and eight books with AMS, including Problems and Theorems in Linear Algebra, Intuitive Topology, Knots, Links, Braids, and 3-Manifolds (jointly with A. B. Sossinsky), and Elliptic Functions and Elliptic Integrals (jointly with Yu. Solovyev).
作者簡介(中文翻譯)
維克多·普拉索洛夫（Victor Prasolov），生於1956年，是莫斯科獨立大學的數學專任教師。他與施普林格（Springer）出版了兩本書，分別是《多項式》（Polynomials）和《代數曲線：模空間的方向》（Algebraic Curves. Towards Moduli Spaces，與M. E. Kazaryan及S. K. Lando共同編著），以及與美國數學學會（AMS）出版的八本書，包括《線性代數中的問題與定理》（Problems and Theorems in Linear Algebra）、《直觀拓撲學》（Intuitive Topology）、《結、鏈、編織與三維流形》（Knots, Links, Braids, and 3-Manifolds，與A. B. Sossinsky共同編著）和《橢圓函數與橢圓積分》（Elliptic Functions and Elliptic Integrals，與Yu. Solovyev共同編著）。
