This book, based on a graduate course on Riemannian geometryand analysis onmanifolds, given in Paris, covers the topicsof differential manifolds, Riemannian metrics, connections,geodesics and curvature, with special emphasis on theintrinsic features on the subject.Classical results on the relations between curvature andtopology are treated in detail. The bookis quiteself-contained, assuming of the reader only a knowledge ofdifferential calculus in Euclidean space. It containsnumerous exercises with full solutions and a series ofdetailed examples which are picked up again repeatedly toillustrate each new definition or property introduced.This book addresses both the graduate student wanting tolearn Riemannian geometry, and also the professionalmathematician from a neighbouring field who needsinformation about ideas and techniques which are nowpervading many parts of mathematics.
Riemannian Geometry: Volume 0 (Universitext)
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P. Petersen
Riemannian Geometry
"A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics."
—EUROPEAN MATHEMATICAL SOCIETY
--This text refers to the Hardcover edition.
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4 of 12 people found the following review helpful:
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Hard to say,
This review is from: Riemannian Geometry (Universitext) (Paperback)
This was the official 100% recommended, guaranteed text for my Riemannian Geometry class. Supplementing this book with do Carmo's text, I was able to get something out of the class, but I think rereading both of them now would be much better. The condensed one chapter course on manifolds at the beginning of GHL wasn't sufficient to learn/relearn everything I needed to know in order to read it for the first time.
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First Sentence:
1.1 Definition. A subset M Rn+k is an n-dimensional submanifold of class Cp of Rn+k if, for any x M, there exists a neighborhood U of x in Rn+k and a Cp submersion f : U Rk such that U M = f-1(0) (we recall that f is a submersion if its differential map is surjective at each point). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
orientation atlas, isoperimetric profile, strictly positive sectional curvature, acceleration vector field, hyperboloid model, isotropy irreducible, flat tori, isotropy representation, second variation formula, geodesic spray, minimal geodesic, first variation formula, claimed formula, local isometry, unit normal vector field, covering map, coordinate vector fields, isometry group, unit tangent bundle, minimizing geodesic, standard sphere, parallel vector field, injectivity radius, revolution surface, map exp Key Phrases - Capitalized Phrases (CAPs): (learn more)
Anti de Sitter, Elie Cartan, G-invariant Riemannian New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
1.1 Definition. A subset M Rn+k is an n-dimensional submanifold of class Cp of Rn+k if, for any x M, there exists a neighborhood U of x in Rn+k and a Cp submersion f : U Rk such that U M = f-1(0) (we recall that f is a submersion if its differential map is surjective at each point). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
orientation atlas, isoperimetric profile, strictly positive sectional curvature, acceleration vector field, hyperboloid model, isotropy irreducible, flat tori, isotropy representation, second variation formula, geodesic spray, minimal geodesic, first variation formula, claimed formula, local isometry, unit normal vector field, covering map, coordinate vector fields, isometry group, unit tangent bundle, minimizing geodesic, standard sphere, parallel vector field, injectivity radius, revolution surface, map exp Key Phrases - Capitalized Phrases (CAPs): (learn more)
Anti de Sitter, Elie Cartan, G-invariant Riemannian New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 14
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83
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- Riemannian Geometry (v. 171) by Peter Petersen in Back Matter (1), and Back Matter (2)
- Riemannian Geometry (Fields Institute Monographs, 4) by Joachim Lohkamp, Pierre Pansu, and Peter Petersen Gerard Besson in Back Matter (1), and Back Matter (2)
- A Course in Arithmetic (Graduate Texts in Mathematics) by Jean Pierre Serre in Back Matter
- Dynamics on Lorentz Manifolds by Scot Adams in Back Matter
- Riemannian Geometry (De Gruyter Studies in Mathematics) by Wilhelm P. A. Klingenberg in Back Matter
See all 14 books this book cites
- An Introduction to Riemann-Finsler Geometry (Graduate Texts in Mathematics) by David Dai-Wai Bao on page 224, page 382, and Back Matter
- Gromov's Compactness Theorem for Pseude-holomorphic Curves (Progress in Mathematics) by Christoph Hummel in Back Matter (1), Back Matter (2), and Back Matter (3)
- Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space (Porter Lectures) by Shmuel Weinberger on page 111, and page 158
- Geometric Methods for Quantum Field Theory by Hernan Ocampo on page 114, and page 359
- A Course in Credibility Theory and its Applications (Universitext) by Hans Bühlmann in Back Matter
See all 83 books citing this book
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