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 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.

First book to outline the history of both differential and complex geometry in parallel

Includes quotes and scans from original documents

Considers mathematical knowledge known at the time of the key geometers

Includes supplementary material: sn.pub/extras

Includes supplementary material: sn.pub/extras

Contenu
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.