Differential and Complex Geometry: Origins, Abstractions and Embeddings

1. Auflage 2017
ISBN: 978-3-319-58183-5
Verlag: Springer International Publishing

Buch, Englisch, 319 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 6269 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Wells, Jr.

Wells, Jr., Raymond O.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.