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An Introduction to Riemannian Geometry

Author: Leonor Godinho

Publisher: Springer

Published: 2014-07-26

Total Pages: 476

ISBN-13: 3319086669

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Riemannian Manifolds

Author: John M. Lee

Publisher: Springer Science & Business Media

Published: 2006-04-06

Total Pages: 232

ISBN-13: 0387227261

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This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Introduction to Riemannian Manifolds

Author: John M. Lee

Publisher: Springer

Published: 2019-01-02

Total Pages: 437

ISBN-13: 3319917552

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Riemannian Geometry

Author: Isaac Chavel

Publisher: Cambridge University Press

Published: 2006-04-10

Total Pages: 4

ISBN-13: 1139452576

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This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

An Introduction to Riemann-Finsler Geometry

Author: D. Bao

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 453

ISBN-13: 1461212685

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This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

Author: William Munger Boothby

Publisher: Gulf Professional Publishing

Published: 2003

Total Pages: 444

ISBN-13: 9780121160517

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The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields

Riemannian Geometry

Author: Peter Petersen

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 443

ISBN-13: 1475764340

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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 specialise in Riemannian geometry. Instead of variational techniques, the author uses a unique approach, emphasising distance functions and special co-ordinate systems. He also uses standard calculus with some techniques from differential equations to provide a more elementary route. Many chapters contain material typically found in specialised texts, never before published in a single source. 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 - including sections on convergence and compactness of families of manifolds. Thus, 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.

Riemannian Geometry

Author: Isaac Chavel

Publisher: Cambridge University Press

Published: 1995-01-27

Total Pages: 402

ISBN-13: 9780521485784

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This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.

Riemannian Geometry

Author: Manfredo do Carmo

Publisher: Birkhäuser

Published: 2013-01-09

Total Pages: 0

ISBN-13: 9781475722031

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Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.

An Introduction to Riemannian Geometry and the Tensor Calculus

Author: Charles Ernest Weatherburn

Publisher: CUP Archive

Published: 1938

Total Pages: 214

ISBN-13:

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