Differential and Complex Geometry: Origins, Abstractions and Embeddings

Differential and Complex Geometry: Origins, Abstractions and Embeddings by Raymond O. Wells, Jr.

Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed exa...

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Bibliographic Details
Main Author: Wells, Jr., Raymond O. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
Edition:1st ed. 2017.
Series:Springer eBook Collection.
Subjects:
Differential geometry.
Global analysis (Mathematics).
Manifolds (Mathematics).
Functions of complex variables.
Projective geometry.
Algebraic topology.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Introduction
  • Part I. Geometry in the Age of Enlightenment
  • Algebraic Geometry
  • Differential Geometry
  • Part II. Differential and Projective Geometry in the Nineteenth Century
  • Projective Geometry
  • Gauss and Intrinsic Differential Geometry
  • Riemann's Higher-Dimensional Geometry
  • Part III. Origins of Complex Geometry
  • The Complex Plane
  • Elliptic and Abelian Integrals
  • Elliptic Functions
  • Complex Analysis
  • Riemann Surfaces
  • Complex Geometry at the End of the Nineteenth Century
  • Part IV. Twentieth-Century Embedding Theorems
  • Differentiable Manifolds
  • Riemannian Manifolds
  • Compact Complex Manifolds
  • Noncompact Complex Manifolds.

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