About this product

Product Identifiers

PublisherSpringer Berlin / Heidelberg

ISBN-103540653171

ISBN-139783540653172

eBay Product ID (ePID)2256769

Product Key Features

Number of PagesXxiii, 824 Pages

Publication NamePanoramic View of Riemannian Geometry

LanguageEnglish

SubjectGeometry / Non-Euclidean, Geometry / Differential

Publication Year2003

TypeTextbook

AuthorMarcel Berger

Subject AreaMathematics

FormatHardcover

Dimensions

Item Weight50.7 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2003-059588

TitleLeadingA

Dewey Edition22

ReviewsFrom the reviews:"In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. â€¦ the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading." (A.Cap, Monatshefte fÃ¼r Mathematik, Vol. 145 (4), 2005) "Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures â€¦ . Marcel Berger's book is an overview of this enormous subject. â€¦ Virtually everything is illustrated with clear and useful diagrams â€¦ . This is the sort of book one could dip into or refer to over a period of years." (Peter Giblin, The Mathematical Gazette, March, 2005)"Marcel Berger's A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry â€¦ . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. â€¦ the book concludes with a massive and extremely useful bibliography of 1310 items." (Robert Osserman, SIAM Review, Vol. 47 (1), 2005)"This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. â€¦ A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining â€¦ which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry â€¦ ." (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004)"This book is really a panorama. â€¦ the reading creates pleasure for the interested reader. â€¦ the book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." (JÃ¼rgen Eichhorn, Mathematical Reviews, 2004 h)"Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. â€¦ enables the reader to obtain a sweeping panoramic view of almost the entirety of the field." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003), From the reviews: "In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. ... the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading." (A.Cap, Monatshefte für Mathematik, Vol. 145 (4), 2005) "Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures ... . Marcel Berger's book is an overview of this enormous subject. ... Virtually everything is illustrated with clear and useful diagrams ... . This is the sort of book one could dip into or refer to over a period of years." (Peter Giblin, The Mathematical Gazette, March, 2005) "Marcel Berger's A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry ... . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. ... the book concludes with a massive and extremely useful bibliography of 1310 items." (Robert Osserman, SIAM Review, Vol. 47 (1), 2005) "This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. ... A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining ... which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry ... ." (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004) "This book is really a panorama. ... the reading creates pleasure for the interested reader. ... the book has intrinsic value for a student as well as for an experiencedgeometer. Additionally, it is really a compendium in Riemannian Geometry." (Jürgen Eichhorn, Mathematical Reviews, 2004 h) "Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. ... enables the reader to obtain a sweeping panoramic view of almost the entirety of the field." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003), From the reviews: "In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. a? the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading." (A.Cap, Monatshefte f'r Mathematik, Vol. 145 (4), 2005) "Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures a? . Marcel Bergera's book is an overview of this enormous subject. a? Virtually everything is illustrated with clear and useful diagrams a? . This is the sort of book one could dip into or refer to over a period of years." (Peter Giblin, The Mathematical Gazette, March, 2005) "Marcel Bergera's A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry a? . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. a? the book concludes with a massive and extremely useful bibliography of 1310 items." (Robert Osserman, SIAM Review, Vol. 47 (1), 2005) "This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. a? A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining a? which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry a? ." (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004) "This book is really a panorama. a? the reading creates pleasure for the interested reader. a? the book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." (J'rgen Eichhorn, Mathematical Reviews, 2004 h) "Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. a? enables the reader to obtain a sweeping panoramic view of almost the entirety of the field." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003), From the reviews: "In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. â€¦ the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading." (A.Cap, Monatshefte fÃ¼r Mathematik, Vol. 145 (4), 2005) "Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures â€¦ . Marcel Berger's book is an overview of this enormous subject. â€¦ Virtually everything is illustrated with clear and useful diagrams â€¦ . This is the sort of book one could dip into or refer to over a period of years." (Peter Giblin, The Mathematical Gazette, March, 2005) "Marcel Berger's A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry â€¦ . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. â€¦ the book concludes with a massive and extremely useful bibliography of 1310 items." (Robert Osserman, SIAM Review, Vol. 47 (1), 2005) "This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. â€¦ A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining â€¦ which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry â€¦ ." (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004) "This book is really a panorama. â€¦ the reading creates pleasure for the interested reader. â€¦ the book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." (JÃ¼rgen Eichhorn, Mathematical Reviews, 2004 h) "Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. â€¦ enables the reader to obtain a sweeping panoramic view of almost the entirety of the field." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003), From the reviews: "In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. ... the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading." (A.Cap, Monatshefte fr Mathematik, Vol. 145 (4), 2005) "Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures ... . Marcel Berger's book is an overview of this enormous subject. ... Virtually everything is illustrated with clear and useful diagrams ... . This is the sort of book one could dip into or refer to over a period of years." (Peter Giblin, The Mathematical Gazette, March, 2005) "Marcel Berger's A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry ... . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. ... the book concludes with a massive and extremely useful bibliography of 1310 items." (Robert Osserman, SIAM Review, Vol. 47 (1), 2005) "This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. ... A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining ... which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry ... ." (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004) "This book is really a panorama. ... the reading creates pleasure for the interested reader. ... the book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." (Jrgen Eichhorn, Mathematical Reviews, 2004 h) "Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. ... enables the reader to obtain a sweeping panoramic view of almost the entirety of the field." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003), From the reviews: "In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. ... the book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading." (A.Cap, Monatshefte für Mathematik, Vol. 145 (4), 2005) "Riemannian geometry has become a vast subject, influencing, famously, the development of general relativity and, more recently, the classification of 3-manifolds by hyperbolic structures ... . Marcel Berger's book is an overview of this enormous subject. ... Virtually everything is illustrated with clear and useful diagrams ... . This is the sort of book one could dip into or refer to over a period of years." (Peter Giblin, The Mathematical Gazette, March, 2005) "Marcel Berger's A Panoramic View of Riemannian Geometry is without doubt the most comprehensive, original and idiosyncratic treatise on differential geometry ... . he manages to include the most up-to-date references on even the most classical topics that he presents, and he puts far greater emphasis on applications. ... the book concludes with a massive and extremely useful bibliography of 1310 items." (Robert Osserman, SIAM Review, Vol. 47 (1), 2005) "This book of one of the main contributors to Riemannian geometry has as a first goal to give an overview to most of the living topics of the subject. ... A second goal is to show how many intuitive geometric questions lead to Riemannian geometry in a natural way. In my opinion it is this way of explaining ... which makes the book highly recommendable to students as well as to experienced geometers. Furthermore, this book is clearly an encyclopedia in Riemannian geometry ... ." (F.Manhart, Internationale Mathematische Nachrichten, Issue 197, 2004) "This book is really a panorama. ... the reading creates pleasure for the interested reader. ... the book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." (Jürgen Eichhorn, Mathematical Reviews, 2004 h) "Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. ... enables the reader to obtain a sweeping panoramic view of almost the entirety of the field." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 49 (3-4), 2003)

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal516.3/73

Table Of Content1 Euclidean Geometry.- 2 Transition.- 3 Surfaces from Gauß to Today.- 4 Riemann's Blueprints.- 5 A One Page Panorama.- 6 Metric Geometry and Curvature.- 7 Volumes and Inequalities on Volumes of Cycles.- 8 Transition: The Next Two Chapters.- 9 Spectrum of the Laplacian.- 10 Geodesic Dynamics.- 11 Best Metrics.- 12 From Curvature to Topology.- 13 Holonomy Groups and Kähler Manifolds.- 14 Some Other Important Topics.- 15 The Technical Chapter.- References.- Acknowledgements.- List of Notation.- List of Authors.

SynopsisThis book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS, This book introduces readers to the living topics of Riemannian Geometry and conveying them quickly to the main results known to date. The results are stated without detailed proofs but the main ideas involved are described and motivated, affording the reader a sweeping panoramic view of almost the entirety of the field., Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way, following in particular Gauss and Riemann.

LC Classification NumberQA641-670