Lectures on Differential Geometry (Paperback)

Bennett Chow

ISBN 10: 1470478048 / ISBN 13: 9781470478049

Published by American Mathematical Society, Providence, 2024

About this Item

Paperback. Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics.The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern-Gauss-Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincare and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds.The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic. A unified exploration of differential geometry guides readers through submanifolds, Riemannian spaces, and advanced geometric analysis. It covers smooth manifolds, curvature, harmonic functions, and flows like curve shortening and Ricci, engaging graduate students and researchers in deeper geometrical insights. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781470478049

Bibliographic Details

• Title: Lectures on Differential Geometry (Paperback)
• Publisher: American Mathematical Society, Providence
• Publication Date: 2024
• Language: English
• ISBN 10: 1470478048
• ISBN 13: 9781470478049
• Binding: Paperback
• Condition: new

About this title

Synopsis

Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics. The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern–Gauss–Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincaré and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds. The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic.