Differential and Complex Geometry: Origins, Abstractions and Embeddings

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Springer, 01.08.2017 - 319 Seiten
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 examination of the seminal contributions to differential and complex geometry up to the twentieth-century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash.

Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.
 

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Inhalt

Part I Geometry in the Age of Enlightenment
2
1 Algebraic Geometry
5
2 Differential Geometry
17
Part II Differential and Projective Geometry in the Nineteenth Century
31
3 Projective Geometry
33
4 Gauss and Intrinsic Differential Geometry
48
5 Riemanns HigherDimensional Geometry
59
Part III Origins of Complex Geometry
71
9 Complex Analysis
113
10 Riemann Surfaces
137
11 Complex Geometry at the End of the Nineteenth Century
159
Part IV TwentiethCentury Embedding Theorems
166
12 Differentiable Manifolds
175
13 Riemannian Manifolds
186
14 Compact Complex Manifolds
211
15 Noncompact Complex Manifolds
269

6 The Complex Plane
74
7 Elliptic and Abelian Integrals
83
8 Elliptic Functions
96

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