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Differential and Complex Geometry: Origins, Abstractions and Embeddings
ISBN-13:
9783319581842
Veröffentl:
2017
Seiten:
319
Autor:
Jr. Wells
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
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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