Differential and Complex Geometry: Origins, Abstractions and Embeddings
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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| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2017.
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| Edition: | 1st ed. 2017. |
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| Online Access: | https://doi.org/10.1007/978-3-319-58184-2 |
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.