Differential and Complex Geometry: Origins, Abstractions and Embeddings

• Κύριος συγγραφέας: Wells, Jr., Raymond O. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Θέματα: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Functions of complex variables.; Differential geometry.; Projective geometry.; Algebraic topology.; Differential Geometry.; Global Analysis and Analysis on Manifolds.; Several Complex Variables and Analytic Spaces.; Projective Geometry.; Algebraic Topology.

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 exa...

Πίνακας περιεχομένων:

• 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.