An edition of Riemannian manifolds (1997)

Riemannian manifolds

an introduction to curvature

Locate

My Reading Lists:

Create a new list

Check-In

×Close
Add an optional check-in date. Check-in dates are used to track yearly reading goals.
Today


Buy this book

Last edited by MARC Bot
July 12, 2024 | History
An edition of Riemannian manifolds (1997)

Riemannian manifolds

an introduction to curvature

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 study of Riemannian manifolds.

The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the curvature tensor as a way of measuring whether a Riemannian manifold is locally equivalent to Euclidean space. Submanifold theory is developed next 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 the characterization of manifolds of constant curvature.

This unique volume will appeal especially 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.

Publish Date
Publisher
Springer
Language
English
Pages
224

Buy this book

Previews available in: English

Book Details


Edition Notes

Includes bibliographical references (p. [209]-211) and index.

Published in
New York
Series
Graduate texts in mathematics ;, 176

Classifications

Dewey Decimal Class
516.3/73
Library of Congress
QA649 .L397 1997, QA641-670

The Physical Object

Pagination
xv, 224 p. :
Number of pages
224

ID Numbers

Open Library
OL668731M
Internet Archive
riemannianmanifo00leej
ISBN 10
038798271X, 0387983228
LCCN
97014537
OCLC/WorldCat
36800559
Library Thing
1063702
Goodreads
5064073
1969547

Community Reviews (0)

Feedback?
No community reviews have been submitted for this work.

Lists

This work does not appear on any lists.

History

Download catalog record: RDF / JSON
July 12, 2024 Edited by MARC Bot import existing book
December 19, 2023 Edited by ImportBot import existing book
December 8, 2022 Edited by MARC Bot import existing book
April 28, 2010 Edited by Open Library Bot Linked existing covers to the work.
December 10, 2009 Created by WorkBot add works page