Lectures On Differential Geometry Yau Schoen Pdf Download
Lectures on Differential Geometry by Richard Schoen and Shing-Tung Yau
Differential geometry is a branch of mathematics that studies the properties of curves, surfaces, and higher-dimensional spaces using techniques such as calculus, linear algebra, and topology. Differential geometry has many applications in physics, engineering, computer science, and other fields.
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One of the most influential books in differential geometry is Lectures on Differential Geometry by Richard Schoen and Shing-Tung Yau. This book is based on lectures given by the authors at the Institute for Advanced Studies at Princeton University in 1984 and 1985. The lectures cover some of the major advances in differential geometry that occurred in the 1970s and 1980s, such as the positive mass theorem, the Calabi conjecture, the minimal surface equation, and the Yamabe problem.
The book consists of six chapters, each focusing on a different topic. The first chapter introduces some basic concepts and tools of differential geometry, such as manifolds, metrics, curvature, geodesics, harmonic functions, and Sobolev spaces. The second chapter discusses the theory of minimal surfaces and its applications to geometric analysis and general relativity. The third chapter studies the existence and uniqueness of solutions to the Einstein equation and the positive mass theorem. The fourth chapter explores the complex Monge-Ampère equation and the Calabi conjecture, which relates the existence of Kähler-Einstein metrics to the stability of complex manifolds. The fifth chapter examines the conformal geometry of Riemannian manifolds and the Yamabe problem, which asks whether every compact manifold admits a metric of constant scalar curvature in its conformal class. The sixth chapter surveys some topics in global differential geometry, such as rigidity theorems, comparison theorems, and index theorems.
The book is intended for graduate students and researchers who have some background in differential geometry and partial differential equations. The book contains many examples, exercises, and references to further reading. The book is also a valuable source of inspiration for new research directions in differential geometry.
The book is available for purchase from various online platforms . However, it is also possible to download a PDF version of the book for free from some websites . However, one should be aware of the potential legal and ethical issues involved in downloading copyrighted material without permission.