From the back cover: This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. About problems with print quality: Many people have reported receiving copies of Springer books, especially from Amazon, that suffer from extremely poor print quality bindings that quickly break, thin paper, and low-resolution printing, for example. Be sure to tell me which edition you're writing about.

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If you're affiliated with a university that has a subscription to Springer's GTM series, you can read the book online. But it's not nearly as good as the second edition! Preview — Riemannian Manifolds by John M. 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 m This text is designed for a one-quarter or one-semester graduate course on Riemannian geometry.

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.

## Introduction to Riemannian Manifolds

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. Get A Copy.

Paperback , pages. Published September 5th by Springer first published January 1st More Details Original Title. Other Editions 5. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Riemannian Manifolds , please sign up. Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Rating details. More filters. Sort order. Jun 05, Josh Jordan rated it it was amazing.

A very nice introduction to Riemannian geometry. Doesn't get bogged down in technicality, but offers exercises and examples that help build intuition. It's a great place to get started learning geomery.

## RIEMANNIAN MANIFOLDS - AN INTRODUCTION TO CURVATURE

Malcolm Lazarow rated it it was amazing Dec 30, Yuri Popov rated it really liked it Apr 04, Curtis Nydegger tekell rated it liked it Dec 07, Kaiser rated it it was amazing Nov 14, Starting with dimension 3, scalar curvature does not describe the curvature tensor completely. Ricci curvature is a linear operator on tangent space at a point, usually denoted by Ric. With four or more dimensions, Ricci curvature does not describe the curvature tensor completely. Explicit expressions for the Ricci tensor in terms of the Levi-Civita connection is given in the article on Christoffel symbols.

The Weyl curvature tensor has the same symmetries as the curvature tensor, plus one extra: its trace as used to define the Ricci curvature must vanish. Although individually, the Weyl tensor and Ricci tensor do not in general determine the full curvature tensor, the Riemann curvature tensor can be decomposed into a Weyl part and a Ricci part. This decomposition is known as the Ricci decomposition, and plays an important role in the conformal geometry of Riemannian manifolds.

From Wikipedia, the free encyclopedia. Main article: Riemann curvature tensor.

## Riemannian Manifolds, An Introduction to Curvature by John M. Lee | | Booktopia

Main article: Sectional curvature. Main article: Curvature form.

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Main article: Scalar curvature. Main article: Ricci curvature. Main article: Weyl tensor. Main article: Ricci decomposition. Various notions of curvature defined in differential geometry. Curvature Torsion of a curve Frenet—Serret formulas Radius of curvature applications Affine curvature Total curvature Total absolute curvature.