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Graduate Texts in Mathematics Ser.: Riemannian Geometry by Peter Petersen (2010, Trade Paperback)
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-101441921230
ISBN-139781441921239
eBay Product ID (ePID)21038720720
Product Key Features
Number of PagesXv, 405 Pages
LanguageEnglish
Publication NameRiemannian Geometry
SubjectGeometry / Non-Euclidean, Geometry / Differential
Publication Year2010
TypeTextbook
Subject AreaMathematics
AuthorPeter Petersen
SeriesGraduate Texts in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight22.8 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
Dewey Edition23
ReviewsFrom the reviews of the second edition:P. PetersenRiemannian Geometry"A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics."-EUROPEAN MATHEMATICAL SOCIETY This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. … After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers BochnerCartan techniques and comparison geometry. Particularly for these aspects it continues to play an outstanding role among textbooks in Riemannian geometry. (M. Kunzinger, Monatshefte für Mathematik, Vol. 154 (1), May, 2008), P. PetersenRiemannian Geometry"A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics."-EUROPEAN MATHEMATICAL SOCIETY, From the reviews of the second edition: P. Petersen Riemannian Geometry "A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics." --EUROPEAN MATHEMATICAL SOCIETY "This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. ... After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers Bochner-Cartan techniques and comparison geometry. Particularly for these aspects it continues to play an outstanding role among textbooks in Riemannian geometry." (M. Kunzinger, Monatshefte für Mathematik, Vol. 154 (1), May, 2008), P. PetersenRiemannian Geometry"A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics." â€�EUROPEAN MATHEMATICAL SOCIETY
Series Volume Number171
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.373
Table Of ContentRiemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holonomy.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.
SynopsisIntended for a one year course, this volume serves 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. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject. Important additions to this new edition include: * A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; * An increased number of coordinate calculations of connection and curvature; * General fomulas for curvature on Lie Groups and submersions; * Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger; * Several recent results about manifolds with positive curvature. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type." - Bernd Wegner, Zentralblatt, Intended for a one year course, this volume serves 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. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. Important additions to this new edition include: - A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise - An increased number of coordinate calculations of connection and curvature - General fomulas for curvature on Lie Groups and submersions - Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger - Several recent results about manifolds with positive curvature, Designed for a one year introductory course, this volume introduces students to the important techniques and theorems of Riemannian geometry, while presenting sufficient background on advanced topics to appeal to students who wish to specialize in the discipline. The text combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and presents the most up-to-date research. The updated second edition includes such new material as: A completely new coordinate-free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgotten proof by Berger; several recent results regarding manifolds with positive curvature., This comprehensive introduction to Riemannian Geometry offers a detailed and engaging account of the topic, plus numerous exercises and examples. It combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and reviews the latest research.
LC Classification NumberQA641-670
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