Riemannian Manifolds

An Introduction to Curvature

By: John M. Lee

Write A Review

Hardcover | 5 September 1997

At a Glance

Hardcover
248 Pages

Dimensions(cm)
24.77 x 16.51 x 1.91

Hardcover

$109.75

or 4 interest-free payments of $27.44 with

Ships in 5 to 7 business days

This text is designed for a one-quarter or one-semester graduate course on Riemannian geometry. It focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the Riemann curvature tensor, before moving on to submanifold theory, in order to give the curvature tensor a concrete quantitative interpretation. The remainder of the text is devoted to proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose- Hicks theorem. This unique volume will especially appeal to students by presenting a selective introduction to the main ideas of the subject in an easily accessible way. The material is ideal for a single course, but broad enough to provide students with a firm foundation from which to pursue research or develop applications in Riemannian geometry and other fields that use its tools. Of special interest are the "exercises" and "problems" dispersed throughout the text. The exercises are carefully chosen and timed so as to give the reader opportunities to review material that has just been introduced, to practice working with the definitions, and to develop skills that are used later in the book. The problems that conclude the chapters are generally more difficult. They not only introduce new material not covered in the body of the text.

Industry Reviews

"This book is very well writen, pleasant to read, with many good illustrations. It deals with the core of the subject, nothing more and nothing less. Simply a recommendation for anyone who wants to teach or learn about the Riemannian geometry."
Nieuw Archief voor Wiskunde, September 2000

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Analytic Geometry

Preface
What Is Curvature?	p. 1
Review of Tensors, Manifolds, and Vector Bundles	p. 11
Definitions and Examples of Riemannian Metrics	p. 23
Connections	p. 47
Riemannian Geodesics	p. 65
Geodesics and Distance	p. 91
Curvature	p. 115
Riemannian Submanifolds	p. 131
The Gauss-Bonnet Theorem	p. 155
Jacobi Fields	p. 173
Curvature and Topology	p. 193
References	p. 209
Index	p. 213
Table of Contents provided by Blackwell. All Rights Reserved.

Riemannian Manifolds

An Introduction to Curvature

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Differential & Riemannian Geometry

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

Volume 120

Lectures on Differential Geometry I

Differentiable Manifolds

Geometric Methods in Physical Systems

From Differentiable Structures to Applications, the Wisla 22 Winter School and Workshop

Geometry of Integrable Systems

An Introduction

Consensus and Synchronization

From the Euclidean Space and the Circle to Lie Groups

Collected Papers of Y. Matsushima

SERIES IN PURE MATHEMATICS

An Introduction to Sympletic Geometry

Graduate Studies in Mathematics

A Course in Differential Geometry

Graduate Studies in Mathematics

Concise Complex Analysis

Topics in Integral Geometry

Series in Pure Mathematics

Two Reports on Harmonic Maps

Harmonic Maps

Introductory Differential Geometry for Physicists

The Arnoldfest : Proceedings of a Conference in Honour of V. I. Arnold for His 60th Birthday

Fields Institute Communications

Least Action Principle of Crystal Formation of Dense Packing Type and the Proof of Kepler's Conjecture

Nankai Tracts in Mathematics

Lectures on Chern-Weil Theory and Witten Deformations

Nankai Traits in Mathematics

Backlund and Darboux Transformations : The Geometry of Solitons: AARMS-CRM Workshop, June 4-9, 1999, Halifax, N. S., Canada

Crm Proceedings and Lecture Notes

Chirurgie des Grassmanniennes

Crm Monograph Series

Trends in Complex Analysis, Differential Geometry and Mathematical Physics

Surfaces with Constant Mean Curvature

Translations of Mathematical Monographs

Interpolation and Sampling in Spaces of Analytic Functions

University Lecture Series

Sources of Hyperbolic Geometry

History of Mathematics

Web Theory and Related Topics

Lectures on Elliptic and Parabolic Equations in Holder Spaces

Graduate Studies in Mathematics

This product is categorised by