About this product

Product Identifiers

PublisherSpringer

ISBN-100387982124

ISBN-139780387982120

eBay Product ID (ePID)1094145

Product Key Features

Number of PagesXvi, 456 Pages

LanguageEnglish

Publication NameRiemannian Geometry

Publication Year1997

SubjectGeometry / Non-Euclidean, Geometry / Differential

TypeTextbook

Subject AreaMathematics

AuthorPeter Petersen

SeriesRiemannian Geometry Ser.

FormatHardcover

Dimensions

Item Height1 in

Item Weight28.7 Oz

Item Length9.4 in

Item Width6.3 in

Additional Product Features

Intended AudienceCollege Audience

LCCN97-005786

ReviewsP. Petersen Riemannian Geometry "A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics." a?EUROPEAN MATHEMATICAL SOCIETY

Dewey Edition23

Series Volume NumberVol. 171

IllustratedYes

Dewey Decimal516.373

Table Of ContentContents: Introduction.- Riemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holony.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.- Appendices. A: DeRham Cohomology. B: Principal Bundles. C: Spinors.- Bibliography.

SynopsisThis book is intended for a one year course in Riemannian Geometry. It will serve as a single source, introducing students to the important techniques and theorems while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian Geometry. Instead of variational techniques, the author uses a unique approach emphasizing distance functions and special coordinate systems. He also uses standard calculus with some techniques from differential equations, instead of variational calculus, thereby providing a more elementary route for students. Many of the chapters contain material typically found in specialized texts and never before published together in one source. Key sections include noteworthy coverage of: geodesic geometry, Bochner technique, symmetric spaces, holonomy, comparison theory for both Ricci and sectional curvature, and convergence theory. This volume is one of the few published works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory as well as presenting the most up-to-date research including sections on convergence and compactness of families of manifolds. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help to motivate readers to deepen their understanding of the subject., Intended for a one year course in Riemannian Geometry, this book deviates in some ways from the standard path. Instead of discussing variational calculus, the author introduces a more elementary approach which simply uses standard calculus together with some techniques from differential equations. This book should appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help the readers to deepen their understanding of the subject., This book is meant for a one year course in Riemannian Geometry. The approach the author has taken deviates in some ways from the standard path. Instead of discussing variational calculus, the author introduces a more elementary approach which simply uses standard calculus together with some techniques from differential equations. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help the readers to deepen their understanding of the subject.

LC Classification NumberQA649.P386 1998