RIEMANNSCHE GEOMETRIE (GRADUIERTENTEXTE IN MATHEMATIK, VOL. Von Peter Petersen

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ISBN-10
0387292462
Book Title
Riemannian Geometry (Graduate Texts in Mathematics, Vol. 171)
ISBN
9780387292465
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Springer
ISBN-10
0387292462
ISBN-13
9780387292465
eBay Product ID (ePID)
51588943

Product Key Features

Number of Pages
Xv, 405 Pages
Language
English
Publication Name
Riemannian Geometry
Subject
Geometry / Non-Euclidean, Geometry / Differential
Publication Year
2006
Features
Revised
Type
Textbook
Subject Area
Mathematics
Author
Peter Petersen
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover

Dimensions

Item Height
0.4 in
Item Weight
60 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
2006-923825
Dewey Edition
23
Reviews
P. Petersen Riemannian Geometry "A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics." a?EUROPEAN MATHEMATICAL SOCIETY, From 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), 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. Petersen Riemannian Geometry "A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics." ?EUROPEAN MATHEMATICAL SOCIETY, P. PetersenRiemannian Geometry"A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics."EUROPEAN MATHEMATICAL SOCIETY
Series Volume Number
171
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
516.373
Edition Description
Revised edition
Table Of Content
Introduction.- Riemannian 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.- Appendix A: De Rham Cohomology.- Bibliography.- Index.
Synopsis
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. 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 ideaabout 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. 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, This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (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 integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature., 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. 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, 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 Number
QA641-670

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