Differential and Complex Geometry: Origins, Abstractions and Embeddings

ISBN-13: 9783319581835 / Angielski / Twarda / 2017 / 319 str.

Raymond O. Jr. Wells

Opis

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.

Recenzje

"The author's writing style is generally clear and inviting ... . This is a valuable book. There is sure to be something useful in it for anybody who is interested in geometry, topology, analysis or the history of mathematics." (Mark Hunacek, MAA Reviews, February, 2018)

"The book under review paves a wonderful pathway for introducing this fundamental chapter of mathematics to students: one can use this well-written volume to explain why certain results in differential and complex geometry are so crucial and important. This volume, a superb addition to the existent literature, is a work that should find its place in the library of every geometer and every topologist at work today." (Bogdan D. Suceava, Mathematical Reviews, 2018)

"The book provides the reader with both historical and technical information regarding various sub-fields of differential and complex geometry. Undoubtedly, the author spent a lot of time researching the tackled subjects and presenting notions in such a clear and fluent way within the manuscript ... . Differential and Complex Geometry: Origins, Abstractions and Embeddings is a rather valuable and extensive work bringing together research topics which are usually studied separately." (Diana Maimut, zbMATH, 2018)

Spis treści

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.